RE: rifled shotgun with rifle sights
You can shoot a rifled slug through a rifled barrel if you want, it will not harm the barrel. It just makes a huge mess and is a pain to clean. Leads up the barrel something awful, but it won't hurt it. I do it out of my H&R ultra sometimes, it actually shoots them pretty well out to 100 yards. A few companies actually make rifled slugs for rifled barrels that either have a harder alloy or a coating on the slug to reduce fouling.
Sabots are much better, but cost more than twice as much.
Shooting shot through a rifled barrel will not harm it either, just like the rifled slug, lead is softer than your hardened steel barrel so no damage will be done. However it is a complete waste of money because it will not pattern worth a darn. The rifling will spin the shot and leave a large hole in the pattern, a very large pattern at that since there is no choke in a rifled barrel. I guess if you wanted to shoot something at point blank range it might work, but much beyond 10 or 15 feet it's worthless.
Here are my suggestions for what you just described. Either save up the money and get a mossberg combo model with a cantilever mount fully rifled barrel and a field barrel. The rifled barrel comes with a mount on the barrel for the scope so you can just take the barrel and scope off without effecting point of aim. ( Still check it every year to make sure though!) And this set up will also come with a smooth bore barrel and three chokes for bird and small game hunting. Probably around 300 bucks or so minus the scope. You can get a remington 870 version as well, but it will cost a tadd more than the mossberg. Both are fine guns for the money.
Another option is getting a single shot like a H&R with a rifled barrel and then order a shot barrel with it. This may cheaper than the pump gun, but will limit you to a single shot. Price will depend on what version you want to get. You can get a heavy barrel with a scope mount, or a lighter version with open sights. Keep in mind the light ones kick like the dickens with slugs. And if you get the heavy barrel version get a 20 ga rifled slug barrel, and a 12 or 20 ga bird barrel. If you get the 12 ga heavy barrel the frame is different and the only bird barrel you can use is a 10 ga. A 20 ga with modern sabots is more than enough for deer out to 100 yards.
I don't think you are going to get any of these for 200 bucks though.
If you only want to shoot deer at say 50 or 60 yards you could just get a smooth bore gun and shoot rifled slugs out of it for deer. Or buckshot if it's legal in your state. I don't care for buckshot much myself though.
You really need to just get out there and see what your local gun stores have. A good gun store should be able to answer any of your questions (not Dick's, walmart, myers or even gander mountain in some cases. I mean a real gun store with knowledgeable people behind the counter.
My opinions anyway.
Paul