Your choice in planes can be mostly decided by two things: whether or not you want to PSM, and which special weapons you want to use ("none" is a perfectly acceptable answer). Planes are conventionally divided into two categories: ENERGY FIGHTERS and PSM FIGHTERS. Right until the very highest skill ceilings, any aircraft can be viable in MP, and thus the most useful things to learn are firing angles and energy management; nevertheless, differing performance will definitely have an impact on your effectiveness, and you must know each aircraft's ideal speeds for turning.
Refer to the general /aceg/ multiplayer guide for builds. Superplanes won't be covered in this guide, because they're all PSM-capable and extremely manoeuvrable - but, funnily enough, some normal planes can easily out-turn them. I will also refuse to recommend QAAM, EML, and SASM, because you won't learn anything useful at all from using them - they essentially do all the work for you.
These are the three most manoeuvrable energy fighters in the base game.
Rafale
For some unfathomable reason, it's THE most manoeuvrable plane in the game, bar none. Only PSMing can beat a highly skilled Rafale user. Coupled with its extremely lethal HCAAs, this is the definitive dogfighter in AC7. It turns best between 600 and 1000 kph.
F-15E
Unlike the F-15C, which is a pretty normal plane, the Strike Eagle/Mudhen is essentially on the same level as the Rafale (imperceptibly lower pitch rate, higher acceleration). Its 6AAMs are surprisingly capable missiles: they thoroughly outperform standard MSLs, and can be used both against single targets and whole furballs. It turns best between 600 and 1000 kph.
MiG-21bis
Paradoxically, the MiG-21 in AC7 is an absolute beast of a plane, and people are misled into thinking it is a low-tier plane by the stat bars in the hangar. Using it in any rooms with a cost limit of 2250 or below is considered bad form, to say the least - because it will completely trash anyone else. MGP is the logical choice for close dogfighting, because it leverages the plane's ridiculous manoeuvrability. Just stay above 600 kph: its ideal speed window is very generous, and will allow you to keep turning hard even in a protracted engagement, but its engines are a bit lacklustre.
PSMing is extremely powerful if you are in a duel, or you are not currently at risk of getting shot at by someone else. In a 1v1, while it's not invincible, you will probably have to work five times harder than the PSM player to win if you're not in a Rafale or Mudhen; if you do use the meta planes, you'll be merely at a slight disadvantage if the PSM player doesn't use chaining. If the other guy is chaining PSMs, the best option would be to not bother with 1v1ing him, and instead getting him while he's distracted - and if he comes gunning for you, go evasive until he loses interest or gets killed by someone else.
These are the most used PSM fighters:
Su-35 and 37
Respectively equipped with 6AAMs or HPAAs, the 35 is slightly more manoeuvrable.
Su-57
Its standard missiles are delayed (because the weapon bays only open when you press the button to fire) and 4AAMs are completely unsuitable for close-range fighting (because they get a delay to homing for the first second after firing), but it's extremely manoeuvrable and has access to PLSL. If you get to knife range, you can PSM and put your nose onto whatever enemy you want to kill.
MiG-29
HPAAs on a much cheaper platform, at the cost of pitch rate and only being half-PSM capable (it can only do cobras, not Kulbits).