Caitlin is an interesting supporter with a very limited use case. , it's a worse Juniper
Unfortunately, as far as supporters go, Copycat is an outclassed card in Legacy. The prevalence of N and PONT in all decks mean that your opponent's hand isn't ever going to amass cards over time or stay at a large size. This means that a Copycat is almost always going to be drawing 6 or less cards, so theres no reason to play it over your own Ns and PONTs. An exception exists for Yanmega Prime decks to match hand sizes with the opponent every turn to activate Insight.
Exeggcute is an excellent card. The concept of freely grabbing a card from your discard pile into your hand as many times as you like with no drawbacks is very powerful. A lot of decks love using Exeggcute to better manage what resources they discard off of Ultra Ball, Junk Arm, Computer Search, and Superior Energy Retrieval. Including a single copy of Exeggcute means that you effectively change these cards' "discard 2" cost down to 1. Egg can also be useful in numerous decks outside of its interactions with item cards. Empoleon can Diving Draw away an egg every turn instead of cards it wants to hold on to. Weavile can recycle 4 eggs for its Villify attack every turn for a guaranteed damage floor of 120. Yanmega Prime can use egg as a way to increase its hand size if it comes up short of a free attack with Insight. However, out of every Pokémon in your deck, Exeggcute is usually the one you want to set face down as your active the least, and you should be aware of the advantage you give your opponent when you start with it. Most importantly, never expect your opponent to send your egg to the discard pile for you. If you can tell that your opponent is avoiding taking a knockout, don't be afraid to attach & retreat if the situation allows it. One other thing that's outside of your control is getting laserbanked, which is a very real threat and will cost you games eventually. While egg can be recommended in a large chunk of the format's decks, it doesn't need to be thrown into everything as a staple 1-of. In decks that only utilize egg for its synergy with item cards, you have to consider how much egg, as a card that takes up a deck slot, is going to be saving you throughout the game. If you're running the standard count of items, something that might look similar to 4 Junk Arm, 1 Computer Search, and anywhere from 1-3 Ultra Ball, you probably don't need egg. If you're playing a deck that doesn't mind thinning its hand to use Tropical Beach, or sending cards to the discard pile for Dark Patch, Dynamotor, and Thundurus-EX's Raiden Knuckle, you probably don't need egg. A good example of a deck that maximizes its use of egg are Magnezone Prime variants. Magnezone often finds itself with resources it doesn't want to discard, and yet it typically needs to run all four of the "discard 2 cards from your hand" items at high counts. Comparatively, Magnezone and decks like it are going to be seeing a lot more value out of a single egg vs. decks that only play it without giving its use further consideration.
Jirachi-EX is a rare example of a Black & White card that play when it was legal in Modified, but doesn't see much play as a staple in modern Legacy lists. On paper, Jirachi seems worthwhile as one of the only ball searchable consistency options, especially in a format where on-board draw is limited. However, the cost of putting it into play always outweighs the benefit. To begin to understand why Jirachi is bad, we need to look at the range of possible supporters Jirachi can search out. Legacy doesn't have a large variety of supporters, so most decks rely on N, PONT, and Juniper, with some using the less common Skyla and Twins. There is Pokémon Collector, but Collector is an outdated card in Legacy, and other basic search options are better. With the exception of Skyla and Twins, Jirachi is only ever being benched to grab a draw supporter. As it stands, Smeargle, Beach, and even Random Receiver fill this role much better. Smeargle is worth one prize, provides continual value over the course of the game, and can be used multiple turns in a row during the first few turns to establish a board very quickly. Random Receiver is an item that can be recycled with Junk Arm and will always grab something, and will essentially have the same effect as Jirachi if you're only listing draw supporters. Tropical Beach, while ending your turn, is still very useful if you aren't in a position to attack or are incapacitated otherwise, and is an amazing card to use in setup decks during the earlygame. Jirachi is also the only one of these options that is shut off by Garbodor, which is always important to consider. But we still haven't gone over the exact two reasons why playing zero Jirachi is better than playing any: being worth two prize cards and having 90 HP. Benching Jirachi means accepting that it will be rabidly hunted down by your opponent at every opportunity. This is so much more impactful in Legacy than benching Lele or Lumineon in modern formats, because the game is both slower and the prize trading between single prize and EX-based decks are so even. Giving a single prize deck the opportunity to gust up a two prizer and knock it out in one hit (there aren't too many relevant Pokémon in format that don't one shot Jirachi, and even if they can't naturally, Silver Bangle will ensure that they can) is the single biggest advantage you can give your opponent, and will guarantee that you lose the prize trade. Even if you're up against something that doesn't play Reversal or Catcher, it's very likely that they'll have another way to KO Jirachi, from anything to Flygon, Genesect-EX's Red Signal, Dusknoir, Raikou-EX, etc. With all of this in mind, though, it is still possible to find specific, justifiable uses for Jirachi. Gothitelle decks can afford to bench Jirachi to grab Twins to establish item lock that in itself serves as protection for Jirachi. Weavile lock variants can safely bench Jirachi for niche use supporters like Hugh or Ghetsis, as that deck aims to control your resources anyways, they can guarantee that Jirachi won't be in danger. It can even be played in extremely fast and oppressive decks that either trade extremely favorably if they high roll or don't expect a response from the opponent and need to maintain speed, like Weavile Eggs or Landogarb (you might need Scoop Up Cyclone in Landogarb's case). Ultimately, if you're an experienced player and have a specific use in mind for Jirachi that the safer and more valuable consistency options can't provide, then go for it.
Mime is a very good card. In the past, bench protection was usually limited to a Stage 1 line and it was almost always one-sided, only protecting your Pokémon from your opponent's attacks. Bench damage is very relevant in Legacy, and you should have a good reason if you're not running a Mime in your deck.
For the most part, PlusPower is a useless and outclassed card. Hypnotoxic Laser is almost a strictly better replacement, because you get the base 1 damage counter from poison (which is already better than PlusPower because it doesn't count as a knockout during your turn in regards to things like Terrakion's Retaliate) and another damage counter from poison going back into your turn, or 3/6 damage counters with Virbank in play. The only times you would play PlusPower is if you're either already playing Laser and want even more damage, (but I don't reccommend this because donk decks are unviable) or because you want your attack specifically to knock out the defending instead of having them die from poison, (this is only really relevant for Lugia-EX so that it can take extra prize cards as the effect of its attack) or if you want to counter decks running Virizion-EX (...don't do this...). Just play laser.
Pokémon Collector is a strange case. While it was a format defining card in Modified for the entire 3 year duration of its legality, it sees very almost zero play in Legacy. Many historical or outdated lists tend to cling to this card, and while it certainly isn't the worst card to be playing, you will get so much more value out of the better alternatives. To understand why Collector is bad, we have to first look at the item search options available. Level Ball is a card that should be a 4 copy inclusion in any deck running a single prize Pokémon line as it will always be free, no cost search for that line's Basic and Stage 1 cards. Ultra Ball is also popular, searching out any Pokémon at the cost of discarding 2 cards from your hand. Pokémon Communication is good in decks that run a high count of Pokémon in various different lines. Dual Ball and Heavy Ball are uncommon options but still see play in decks that run mostly Basic Pokémon and decks that run Pokémon with high retreat costs respectively. One of the most important aspects of item card Pokémon search is that Junk Arm will effectively double the amount of copies of each of these. Using a Level Ball on your first turn, and then using PONT as your supporter to draw into another Level Ball and a Junk Arm for a third will put you in the same place as having used Collector, but now that you've used a draw supporter you get to see other cards you want to see on your first turn, like Escape Rope into Smeargle or Tropical Beach. And if you run Collector instead of a heavy count of item search, you get punished way more for failing to open with a Collector and could instead find yourself using PONT or N turn one and drawing into the Collector you couldn't find, which is now unusable this turn, which puts you a turn behind on setup. Collector is a card that you need to include as a 4-of in order to maximize the chances of seeing it in your opening hand, but 3 of those copies will turn into what is essentially a dead card after you've used your first one. There is one last specific way that people have attempted to run Collector that tries to address and fix all of these problems: running one Collector and a Jirachi-EX along with heavy item search to fish it out of your deck on your first turn. This would be a pretty effective strategy if Jirachi wasn't Jirachi- benching a two prize Pokémon that has such low HP is a death sentence and in most cases is enough to make you automatically lose the game against many top decks.
The Stadium wars in Legacy are pretty uninteresting. If a deck is playing a Stadium, it's almost always either one of Beach, Virbank, or Skyarrow.