This has been on my mind for a while. I really think that Peach is one of the best teammates for Link in teams. The two biggest strengths are that they both occupy space really well, and their moves rack up damage very quickly. Even the way they occupy space is different enough that it complements each other. Link is good at creating pressure beneath a platform, while Peach is good at floating above opponents, or she can d-smash on platforms as well. Because of the way they occupy different spaces, both characters are naturally in the right position often times to extend combos even further. Link can throw his projectiles which Peach can knock opponents into for some extra %. Link can follow up on most of Peach's throw directions and the launch angle(s) of her d-smash, and Peach can throw an aerial out at the end of many of Link's combos.
Both characters have a very good recovery, but one of the major weaknesses of having a good recovery is it leaves your teammate by themselves for a longer period of time. Peach's float ability however allows her to avoid combat more easily than most characters and can wait for Link to return, assuming she isn't trying to deter edgeguarders in the first place. (Perhaps, she stalls until Link gets close and then blocks edge guard attempts) Link is able to help Peach avoid edgeguarding as well with his ranged projectiles. Both characters have diverse recovery options, so it doesn't take much harassment to create an opening back on stage for your partner.
In terms of character match-ups, I think Link and Peach compliment their worry match-ups pretty well. In particular, they both actually help handle the part of their respective match-up vs the spacies that gives them trouble. The biggest issue Link faces vs space animals is the huge shield pressure they have on Link. Link is often easily forced into his shield, and while his sword spin protects him decently horizontally, having pressure from short hop attacks directly on your head covers most of Link's options. This presents a good oppurtunity for Peach to use your amazing aerials. I think her best assist is to float above and d-air, which creates a situation where Fox/Falco must be careful. Trying to continue to pressure Link can result in being d-air'd to n-air'd by Peach which will knock them off stage. Meanwhile, chasing Peach will let Link get directly underneath you, who will start u-airing. If the player flees and even gets nipped by d-air, Link can up-b oos and hit them too. What Link can do for Peach is basically keep the space animal's ground game in check. Grounded space animals are where Link is his strongest against them. They become more prone to silly stuff like grab, up-b, jab, and smashes 'n' stuff. Also a straight boomerang will occupy the ground space pretty well too.
The team does have a weakness though, and that is dealing with seperation. Neither character is very fast or super mobile, so it is hard for either character to get past an opponent and reunite with a teammate. This isn't necessarily always a problem for a top tier character such as Peach, but Link can get pooped on by a lot of things, so without Peach attending him, it's up to the skill of the Link player to not start losing. The best oppurtunity to seperate them both is while one or both of them is recovering. At this point, it is best for the Link or Peach that is still on stage to try and avoid conflict for a while, but at the same time this actually makes it a little easier for the opponent to shut Link/Peach out from his/her partner.
This idea of having Peach as a partner stems from recent experience in experimenting after a tournament, but there also happens to be a highly successful team featuring the duo, Lord HDL and Eval! I don't have any vids of myself doing this team yet, but here are a couple of theirs and I'll try to point out parts of the video to further explain what I mean.
vs Kel/Watty #1
https://www.youtube.com/watch?v=ctINzX_B3Ls
I have no clue what happened and why they ended up on Stadium. This stage looks really good for both Fox and Samus, but oh well. Stage striking does not always put you on the most nuetral stage for the match-up.
0:25 Notice so far that Link is commonly on the ground while Peach is usually close to either platform or on them. This to me is the conventional setup for the team.
0:28, Fox starts shield pressuring Link, but shortly after, Peach floats above. I'm not sure if Peach's presence is what leaves Fox open, but Fox continues to full hop stuff and Link punishes with u-air shortly after
0:30 Samus goes to try and edgeguard Link, but Peach spooks her for just a moment, long enough for Link to secure his way back on stage.
0:39 - 0:50 Link kind of starts ignoring the fact that Peach needs help to harrass Samus instead. Understandably, you cannot ignore either opponent, but HDL lets himself be drawn away from Fox. Luckily, Fox gets greedy and tries to run and u-smash Link, which only lets Peach get back on stage.
0:54 not sure why Fox stopped and u-smashed, but he's horizontal of Link's sheild which means SKRAAAAHHH!! (and Peach's n-air lol)
1:02 Peach is allowed to safely float behind Link as Link prevents Fox from simply running on foot after her.
1:16 - 1:24 The stage transformation encourages the two to split up. Link gets hungry for the kill on Samus leaving Peach to fend off Fox while at high percent. Sadly, both of red team lose a stock here.
1:30 - 1:43 LOLOLOL
Mostly basic stuff happens from this point on. Pretty close game 1, but HDL/Eval take it.
vs Kel/Watty #2
https://www.youtube.com/watch?v=oZazEMtZRPw
0:58 We're about a minute in and both opponents have over 150% damage. Shame we're on dreamland, or they probably wouldn't be still living right now.
1:07 Link accidentally airdodges and who know's what Peach is doing. Oops, Fox gets a double KO.
1:25 Link's in trouble and is forced to hold shield again. Peach comes in with d-air, d-smash and Fox dies.
About this part, the game kind of dissolves into two pairs of single matches going on. Team work stops being emphasized by the red team.
4:02 Boomerang save by Link
Game 2, as the match progressed, the fight started to shift into two sets of singles. Though they picked good match-ups (Link vs Samus, and Peach vs Fox), they were still outed mostly due to that and the other team did exploit them slowly returning to stage, which while not as bad as most teams with good recoveries, is still a weakness.
vs Kel/Watty #3
https://www.youtube.com/watch?v=NLPndvMWx68
HDL and Eval choose Yoshi's Story. Small stage with low platforms. Allows Link and Peach to guard all the space. Very little safe places to be for the opponent and Samus dies much earlier now.
1:25 Fox tries to drop b-air to the ground to edgeguard Peach, but eats sword spin instead. Samus thought it looked good and tasted it too.
2:08 normally, it would be great to just short hop all over Link's head when he's stuck like this, but this damn ***** keeps floating in the way! Sword Spin breaks it up.
3:00 Samus keeps getting hit by Peach. Link follows with projectiles to keep Samus from being very mobile.
3:06 Link tries to protect Peach with a bomb, but misses Fox.
3:28 Watty being a smart player.
3:45 - 3:49 Link launches Fox. Normally this leads to a situation where Link must read where Fox is going to try to escape to, but Peach happens to be where she is needed floating underneath the platform. She covers one of Fox's options and spooks Fox into rolling back towards Link where he eats a nice, beefy d-air.
3:54 Peach is still above, Fox tries to u-smash Link and gets grabbed instead.
Overall, game 3 I think best shows what I am trying to explain. Both Link and Peach provide a more consistant presence for each other that limits their opponents into doing options they want.
Here are some more vids of Link/Peach being piloted by HDL/Eval that I didn't feel like commenting on:
vs LK & Wandering
https://www.youtube.com/watch?v=E7i8_W3TyRE
vs Doh & Chillin
https://www.youtube.com/watch?v=M993hS8OY3I
vs E.Zero & F.H@wk
https://www.youtube.com/watch?v=CMRZN2XekGI