Yes, Saitek ST290 is pretty good beginner joystick. It has most features you need, including numerous programmable buttons costs you around $40. Saitek is well-known amongst flight sim enthusiasts for having realistic feeling of the control movements, especially the throttle.
Alternatively you can try Logitech Extreme 3D Pro Joystick that costs you around $30. This joystick has twist function to control rudder, so you can sway your aim to give better chance of hitting your target. Perfect for non-dedicated Flight simmers.
What we mean by "Quick battle" is an instant mission creator, where you only have to choose your map, your plane (and your flight, how many) and your enemy planes (how many planes, how many squads/flights) then vroooom! Just fly
In Il-2 you'll be at 2,000 m on default (you can customise this as well), about 10 km from the enemy head-to-head by default (you can also customise this) and at the same level also by default (customisable as well). The enemy can have AAA or ground support or ground targets (also customiseable).
That's quick battle.
What you mean is probably single mission, in single mission, your plane is pre-selected, the area is pre-selected, and it has specific objectives (e.g. free flight/roam around, CAP, CAS, bombing, nuisance raid, etc).
