Team Theory
Captain America is a Point character. He greatly benefits from two strong supports, and has very specific needs to thrive. He requires strong horizontal coverage, strong vertical coverage, and assists that help him convert off charging star. He additionally loves to have a damage engine mid (such as Vergil, Spencer, or MODOK), whom he can DHC to off awkward hits in order to secure kills.
Best Friends
Captain America's best friends in no particular order are:
Doctor Doom
Doctor Doom is probably the single best support for Captain America. The Lord of Latveria's Plasma Beam assist is extremely strong for Cap, and if played mid, doom's TACs and hard tags both benefit Cap greatly. If placed on anchor with a damage engine in the middle, Doom's support can still be extremely strong. Hidden Missiles is arguably Cap's single best assist, allowing him to link Hyper Charging Star into Hyper Charging Star, but it requires another horizontal assist to supplement it to justify running it over Plasma Beam. Molecular Shield is the most niche of the three, but it gives cap easy grab confirms and helps to cover his grounded approaches. All in all, cap/doom is an extremely strong pairing and worth your time.
Doctor Strange
Doctor Strange's Bolts of Balthakk is arguably Cap's single best horizontal assist, allowing him to loop charging stars in the corner with ease and aplomb. Captain America can additionally tag into Doctor Strange for palm loops relatively easily off shield slash from midscreen. Cap can link Hyper Charging Star into team super with Vishanti behind him, allowing him to dump meter for huge damage. All in all, Strange is absolutely one of Cap's best friends.
Rocket Raccoon
Rocket Raccoon's Spitfire and Pendulum assists are both outstanding for Captain America, with both being extremely easy to abuse with Backflip. Spitfire helps Cap maintain control over the ground, whilst Log Trap helps him control jump height. Mad Hopper allows Rocket to act as a damage engine for Cap, and Rock n Roll is a good DHC in the corner. All in all, Cap/Rocket is a strong pairing, though you still may want a beam to pair with them.
Vergil
Vergil is arguably the best damage engine for Captain America, with Swords DHC allowing him to easily convert random hyper charging star into a kill. Rapid Slash is additionally an extremely strong assist for Captain America, allowing him to make his charging stars safe on block as it pushes the opponent to full screen. Vergil additionally quite likes Captain America's shield slash assist, which allows him to convert off helmbreaker with high time.
Strider Hiryu
Captain America is one of the best users of Strider Hiryu's Vajra assist in the entire game. With his strong OTG option in L shield slash to pick up off stray vajra hits, strong left/right game thanks to cartwheel, and weakness to fliers, Cap benefits strongly from all aspects of Vajra. He can also protect it fairly well, using H shield slash to prevent opponents from completely demolishing the ninja should they catch him unawares. Captain America has strong assist extensions using Vajra and also can use it for nasty incomings. Amazing pair.
Iron Man
Captain America works very well with his fellow Avenger, Tony Stark. Unibeam has the unique property compared to other beams of holding the opponent in a static position, as well as leaving them standing, both of which are excellent for Cap's combos. Unibeam is one of his best assists, and arguably his single best horizontal assist, but running it comes with the complication that Iron Man is a difficult character to succeed with.
Other Strong Support
Arthur
Arthur's daggers are an excellent choice for Cap, and he benefits greatly from Charging Star assist as well. Cap can DHC into Goddess Bracelet for an excellent - and safe - way out, as well as often using Arthur's ability to loop supers to confirm stay hits into kills. Fantastic pair.
Sentinel
Sentinel's Drones are great for Cap, who can use them to loop supers as well as for their excellent neutral presence. Plasma Storm is a highly damaging DHC to help finish off opponents, and Hyper Sentinel Force is a very safe one. Excellent choice behind Cap.
MODOK
MODOK is an excellent partner for Captain America, giving him a beam assist, a safe DHC, and a damage engine all in one. MODOK and Cap played together landed Cap his highest placement at Evo in the hands of Frutsy, who played MODOK/Cap/Doom.
Iron Fist
Iron Fist's Rising Fang is an excellent choice to complement Cap, who can use it well for mixes and extensions. However, Iron Fist is a terrible anchor, and that is the only position you would want to play him on with Steve Rogers.