I started out with a Remington 870 Express (pump). You can do trap with any shotgun... they all do the same thing.
I now shoot with a CZ Redhead Deluxe and had some custom stock work done (adjustable comb) and had them add a center bead for easy alignment before calling for the trap.
By fit, there's a couple main things...
1. Comb (height of the top of the stock)
2. Cast (cast-on, cast-off, cast-neutral) this is the angle of the stock left to right
3. Cheek position (forward/backward) on the stock
A Browning BT99 is a pretty common recommendation for a starter trap gun, but many people start out with semi autos and pumps (their field guns usually).
Really depends on your budget, sky is the limit ($30,000+). That said, I recently shot a $10-$12000 trap gun and realized I miss with those too.
Here's my adjustable comb:Adjustable Comb by Tom Larkin
by Light Artisan Photography
, on Flickr