All you need to do is search the forums on "rolling planeset" and you will see a pile of threads discussing the merits of controlling plane matchups vs. not. The MA (Main Arena) is the primary place people fight, it's completely free-form, you can get P51D vs P-51D as each "side" has access to all the aircraft. The CT (combat theatre) is a little more structure in plane matchup but still fairly free-form in terms of goals/action. A new arena/game called the Tour of Duty (ToD) is in the works and appears to be more restrictive in terms of plane availability and missions/goals, according to HTC and posts that have been made. No ETA on that yet.
Some very high-end aircraft are generally restricted in the MA, things like the Me262 jet, but overall the "average" aircraft is probably in the mid-late 1944 period. You can fly something earlier war and it will be seriously out-classed in most cases although to some people that is just part of the challenge. There are also exceptions to the rule, some aircraft are just more "useful", specially suited to gameplay, or have a historical element that attracts people. You'll probably find that 90% of what you encounter will be about 10-15 different aircraft though, there are certainly some that are very common.
-Soda