I think opinions are going to vary alot on your questions. First off, whatever brand you choose make sure the gun fits you or it's all for naught. There are alot of different brands out there under 1k. A better option would be to buy a quality used gun rather than a newer cheap gun. I personally shoot a SKB only because I grew up with one.

If you choose to go with 20ga, that will limit your 3" shells. It may be hard to find 3" shells other than 12ga or 10ga.

Also, most modern shotguns will come with choke tubes so you won't have to decide except for skeet-skeet choke.