“Within reason on price” doesn’t help much to narrow it down. You can probably find a beat up but functional savage pump for $100. Or a beat up but functional Remington 1100 for $250. Or a decent Browning over and under for $1,000. Or a nice Caesar Guerrini for $3,500. Or a really nice Krieghoff starting at around $10,000.
Okay, with that dollar amount I would look for a good used semi auto - say a Remington 1100 or a Beretta 390 or 391. You might find a very low end over and under BUT - any over and under for that price is most likely not going to be very well made nor will it have much market acceptance and the resale market, should you choose to sell, will be pretty limited. A decent over and under, say a variation of one of the Browning models, will probably start at around $1,500 or more.
Take a look at gunbroker, gunsinternational, or gunsamerica to begin to get an idea of prices.
If if you lived anywhere close to Indianapolis I’d suggest you stop in to the Indiana Gun Club. I would guess they have one of, if not the biggest, inventories of new and used trap guns in the state. They do have a website where almost all of their guns are listed. You could call and explain your wants/needs.
If you plan on doing quite a bit of shooting and eventually want to get serious shooting registered targets you will probably end up upgrading to an over an under. The more rounds you shoot the better the gun must be constructed to reduce functioning problems. The Remington 1100 and the Berettas are pretty bullet proof but you do have to clean them once in awhile.
One disclaimer. If your trapshooting consists of you and a bunch of your buddies out on the farm shooting some birds thrown from a hand trap - no worries. If your intent is to shoot at a regular trap range with five guys standing on the line there is one concern. Shooting an auto loader means the spent hull is going to be ejected when you fire. If that shell flys far enough to hit the guy standing to your right you aren’t going to be very popular. Especially if you bounce a hull off the stock of some guy’s $10,000 Krieghoff. They make a simple device that controls the empty hull once the shell is fired. Cost is $20 +/- and it just clips on to the receiver.
Lastly, you will handicap your success if you buy a gun with a stock that doesn’t fit you. If you’re halfway serious about shooting and getting good I’d consider a gun with an adjustable comb on the stock.