Assuming that, by matches and PvP Quests, we are only referring to Normal Ranked PvP, here are my suggestions for PvP Quests, which take into account the fact that players who do not complete them are only missing out on additional, totally optional rewards:
3 Daily PvP Quests:
Play 5 matches. Ideally, even if the number ends up being lower, players should always be able to finish all daily PvP Quests if they complete this one. Instead of 5 matches, we can also have X matches, with X being a number between 3 and 5.
Win 3 matches. Likewise, instead of 3 matches, we can have X matches, X being 2 or 3.
The last daily PvP quest can rotate between 1 of these quests:
Play a game with X in your team, X being a random Pokémon. Here are some potential issues that could arise: Players not having X; X being absolutely terrible and almost always constituting a burden; players being forced to borrow Pokémon in order to complete this quest from time to time, which could also increase the risk of potential scammers, given that the lending function currently doesn't work.
Having said that, X can be randomly chosen from the player's PC based on level-100 Pokémon, but some of those will be story Pokémon and will be extremely mediocre, while other players can make sure to have PvP-ready lvl-100 Pokémon just for the sake of doing this quest, so I don't think choosing a Pokémon that the player already has can work.
Another suggestion is to make sure that only fully evolved Pokémon can be mentioned. Moreover, if certain Pokémon, like Unown, can be blacklisted in advance for being too mediocre, I think it is also worth considering.
Play a game without X in your team, X being either the Pokémon that the player used the most the previous day (if there is a way to keep track of this) or a random Pokémon from the Top 25 list.
Play a game with a X-type Pokémon, X being a random type, or play a game without a X-type Pokémon, X being either the type that the player used the most the previous day (if there is a way to keep track of this) or a random type. If considered, I would like certain types, like the Steel type, to have a higher chance to be chosen.
Some other silly but maybe fun ideas:
The "Play 5 matches" and "Win 3 matches" quests could rarely change to "Play 5 matches without X in your team" or "Win 3 matches without using X-type Pokémon." For these particular quests, I do not think imposing a must-have condition (e.g., "Win 3 matches with Bibarel") would necessarily be popular.
Play or win 1 match with a Pokémon starting with the letter X, X being a random letter (Yes, I know X is already a letter, but...).
Play or win 1 match with X Y-type Pokémon, X being the number of Pokémon and Y being the type. X should maybe be capped at 3 or 4, while Y can be any type.
Something worth noting is that some players might be tempted to forfeit immediately in order to complete some of these daily quests. Is it possible to have them complete the match? I understand that it could be a long and frustrating one, though (e.g., against Stall), which is why I am in favor of changing most of these quests from play to win instead.
3 Weekly PvP Quests (that can be completed alongside daily and seasonal PvP quests):
Get a minimum of 100 rating or get a minimum of X rating, X ranging from 80 to 120.
Win X matches with at least Y OT Pokémon in your team, X being a slightly higher number than for daily PvP quests and Y being capped at 3 or 4.
Defeat a player with 100 more rating than you.
Defeat a player from a rival Top 10 guild.
Win X matches with Pokémon that have a total of 600 Y, X being a random number of wins within a certain range and Y being a random Base Stat (HP, Atk, Def, etc.). "600" is an indicative number, but the main issue is Speed, which prevents me from picking something higher (since 6 115-Base Speed Pokémon would not even reach 700 BST).
Alternatively, this can be changed to: Win X matches with Pokémon that have a total of Y Z, X being a random number of wins within a certain range, Y being the BST, and Z being the stat in question. This way, numbers can be tailored according to each stat.
Win X matches with a Pokémon with the ability Y, X being a random number of wins and Y being a weather-inducing ability.
Win X matches in a row, X being at least 3.
Win X matches without using more than Y Pokémon from last season's list of Top 25 (or Top 50) most used Pokémon, X being a random number of wins and Y ranging from 1 to 3.
OHKO X Pokémon, X being a random number. Note: OHKO=One-hit knockout. This means that a Pokémon taking 99% damage (because of Focus Sash or something else) would not count, so be careful with entry hazards, too!
We can also have a different version of this achievement: Have X Pokémon faint without you dealing any direct damage to them, X being a random number.
Win X matches without using any legendary or mythical Pokémon, X being a random number.
Win X matches without using the item Y, X being a random number and Y ideally being one of the player's most regularly used items (e.g., Leftovers, Focus Sash...).
Win X matches without any of your Pokémon having more than Y Z, X being a random number, Y ranging from 60 to 80, and Z being the base stat. An example would be: Win 3 matches without any of your Pokémon having more than 75 Base Speed.
3 Seasonal PvP Quests (that can be completed alongside daily and weekly PvP quests):
Finish the PvP season in the Top 25 Normal Ranked PvP ladder.
Achieve X rating without using your 5 most used Pokémon from last season.
Achieve X rating without using more than Y Pokémon from last season's list of Top 25 most used Pokémon, X being at least 200 and Y ranging from 1 to 3.
Achieve X rating without using any legendary or mythical Pokémon, X being at least 250.
Defeat X players from a rival Top 3 guild, X being a random number (but at least 3).
Win X matches with Y dealing the final blow, X being a random number (but at least 3) and Y being a random Pokémon. This could be really frustrating if Y is a bad Pokémon, but it might encourage some creativity.
Win X matches with none of your Pokémon having a BST higher than Y, X being a random number and Y being a relatively low number as far as BST is concerned.
The first listed seasonal PvP quest should always be present, in my opinion. I am not sure how players would receive their seasonal PvP rewards, though. For example, if they do not interact with a certain NPC (because, let's say, they have to wait for the end of the season to be confirmed as Top 25 players), how will they receive them? Maybe at the start of the next season?
Let's assume 30 days in a given season. This means a total of 90 daily, 12 weekly, and 3 seasonal PvP Quests. I think that PvP daily quests should not grant players additional rewards for completing all of them every day. If each one grants the player 1 PvP Token (or 1 PvP Coin, which might be more appealing as a way to balance this out, since there is a currency exchange cap), 90 PvP Tokens (or 90 PvP Coins) can be earned every season through daily PvP quests alone. I think this is fine. Weekly PvP quests should then grant players 3 PvP Tokens (or 3 PvP Coins) for a total of 36 possible PvP Tokens (or PvP Coins) every season. Finally, as seasonal PvP quests are noticeably more difficult, they should maybe grant players 5 or 10 PvP Tokens (or PvP Coins). I am not sure about the individual number, but players can then earn 15 or 30 PvP Tokens (or PvP Coins) for completing all seasonal quests. However, this is still a relatively low number because I do not know if players will also earn additional rewards for completing all weekly and seasonal PvP quests every time. Assuming no extra Tokens or Coins, the 3 seasonal PvP quests should grant a total of 30 PvP Tokens or (PvP Coins). As such, players can earn up to 156 PvP Tokens (or PvP Coins) for completing every single PvP quests. The numbers can be tweaked later.