The stall buffet kicks in when any part of one of your wings has reached stall condition. Lift is calculated across many individual points on your wings. It is possible to ride through the stall buffet without losing controlled flight and fully stalling one or both wings.
Not only speed, but weight also play an important part in causing stall conditions. A common n00b scenario is to take up a P-51 with 100% fuel, rockets and drop tanks. Let's estimate 3/4 ton of internal fuel, plus external payload to be about 1-1/3 ton of expendable weight on your plane. As soon as you try to maneuver and pull 2G that expendable weight effectively doubles and translates into 2-2/3 ton of wing loading.
Now let's change that scenario to only 50% fuel and no externals. Now to reach that 2-2/3 ton of expendable weight on your wingload, you can pull almost 3.5 Gs! I hope that conveys how much of an effect weight has on handling. This especially applies to US fighters that are heavy to begin with, and have a very large internal fuel capacity.
[edit]I guess I should mention that there is a stall condition called an accellerated stall where you are effectively producing more G load than lift. This can happen at speeds well above stall speed.
For a starter plane I usually suggest the N1K2 as it has forgiving handling characteristics, a strong gun package, multi-stage flaps, and good horsepower. I also suggest the spit 8, 9, and 16, though they are minus the multi-stage flaps, and do have a bit of a rough vertical stall. Both types should give you a good feel for the flight model, and have good enough inherent performance to keep a new player alive longer than either more heavier fighters, or more nimble, but underpowered fighters.