You could go many routes here.

You could go cheap with a single shot H&R.

These guns have alot going for them. They are sturdy and durable. they also are cheap and can be extremely accurate.
The only down side is that they are single shot. But if the guy behind the gun is deadly accurate, then 1 shot is all you need.
however, regardless of how accurate some people might or might not be, the truth is, alot of people like the idea of having 3-5 more shots in the magazine tubeor clip after they let a shot off. Don't ask me why, but from most opinions thatI have heard , this is the case. I hunt deer with an 870 that holds 5 rounds and a 30-06 that holds 5 rounds. Only 1 time out of 22 deer haveI ever had to fire more than 1 shot to kill a deer. But the truth is, I like having the ability to cycle another round in the chamber afterI shoot. Dont ask me why....because i dont know. I never use the extra rounds, but I just like having them.

If pumps are your area of interest, a good 870 or winchester 1300 would be a good choice. Also, mossberg sells pumps at pretty good prices too. You shouldn't have to pay an arm or leg for your slug gun. and these 3 models are pretty reasonable on the price scale. If you buy one in a combo or with interchangable chokes, you will be able to hunt alot more than just big game too. This is also nice if you are on a tight budget.

I would like to put in one of my own opinions about accurate guns. I am a firm believer in the bolt action shotguns. Whether its the savage 210, mossberg 695, marlin 512, or the browning. All of these guns are extremely accurate. And they also offer you 3 shots,instead of the 1 shot from the H&R. You will pay a little more for these than the H&R, but I think they are an all around great choice. All are reasonable price for the exception of the browning.

All of the above guns will serve you well, but just do some thinking about exactly what you will want to be doing and to what methods you will be doing it.