For a first gun I'd recommend a Birmingham boxlock of decent quality. Gamebore export good 2 1/2" shells into the USA - order 1000 and be done.
I just found one for someone - a Rowland Watson built by Westley Richards - mid-weight boxlock ejector, nicely made, fancy back, nice engraving: £1800. To my mind this is a good start that will last a lifetime. Plainer guns of Webley origin will come down in price to around £500 for a non-ejector.
I'd forget about 2" guns or 2-bores as they add to the expense. I don't see why anyone would put 20-bore sleeves into a12 unless they had to to shoot skeet. 12-bore ammo gives you more variety from 21 gram loads up to 32 gram in 2 1/2" chamber cases. 20 bore loads will cost more and patter worse.
