Cricket, what form(s) of trap are you going to shoot? If your primary concern is ATA singles trap or handicap, you can get a nice used Perazzi TM - 1, have lots of change to spare and never have to apologize for the gun no matter where you shoot.
If some form of doubles or 2 shot trap will enter the picture then an U/O is the gun of choice. A minty but used Beretta 682 Gold E X-Trap will use up all of your budget, a new 686 E Trap with adjustable comb will leave you with about a thousand to spare - my personal favourite in the trap gun for the buck department.
If you want something different look at TSE's Fabarm line (nice guns & lots of choices) which are also very good values. Check out the "for sale" postings at your local trap club(s) as well.
For $3,500 I would buy the 686 E Trap with adjustable comb ($2,500 + tax), 10 flats of quality shells (~$500+ tax), a Trius OneStep (a self operated trap flinger $140 + tax) and spend what's left on targets. A man can have a whole lot of fun with a setup like that, and if you lose in competition it won't be because of the gun, or the ability to practice.
Sharptail