If you are using a slug gun, especially a 20 gauge, pick a centerfire rifle in just about any caliber and it will be an upgrade as far as accuracy and effective range go. What action you get may depend on how you hunt. If your shots are close and you do a lot of pushing/drives, a pump or semi-auto may work better for quick follow up shots. If you sit in a stand most of the time and want better accuracy and caliber selection, a bolt action will fit the bill just right. It'll offer more options and be available cheaper depending on make/model. I have 6 deer rifles chambered in .243 Win, .270 Win, .30-06 SPRG (2) and 350 Legend (2). Also have a .223 Rem and .223 Wylde which would work in a pinch, but are not ideal for larger Midwest whitetails. All but two are bolt actions. I hunt stands and am more of a "one shot" kind of guy, so shooting a bolt action does not bother me. The two that are not bolt actions are an AR in 350 Legend and a pump action .30-06 that belonged to my late grandfather.
If someone were to ask me what the best overall deer rifle would be for hunting in Wisconsin inside 200-300 yards, I would tell them to buy a bolt action rifle (probably a Savage 110) in .308 Win or .30-06. Why? Those calibers are common, readily available (.308 is a military round and always being produced) and offer a wide range of bullet weights and configurations (cup and core lead, bonded, monolithic, hollow point, ballistic tip, etc). Factory loadings can be found for both in 110 gr - 220 gr, with many falling in the 150 - 180 gr range, which are perfect for deer. Before the 6.5 Creedmoor guys start spitting BC numbers and efficiency, etc. keep in mind we are talking 200 yards and in...so bullet drop and energy at 500+ yards are irrelevant.
As someone else already stated, the Savage 110 series is a good, accurate workhorse rifle. Topped with a good variable-powered scope (Vortex, Leupold, Redfield, etc.) you would be set for most big game anywhere in North America. Really though, a .270 Win, .243 Win, 7mm-08 and a couple other calibers would work just fine, especially if you use heavy-for-caliber bullets (140-150 gr .270, 95-100 gr .243, 140 gr+ 7mm-08, etc). A 7mm Mag, .300 Win Mag, etc. will burn more powder, punish you at the bench, create bad shooting habits (flinching) and do more damage (ie waste more meat) on game than the aforementioned calibers. The rifles and ammo will also be more expensive. You won't be able to thump your chest and brag that you shoot a whizz-bang magnum, but you'll probably be a better shot and not ruin as much meat. Again, there is no reason to seek out and buy a magnum caliber for shooting a 200 lb or less animal inside 200 yards. Zero. Now, if you move here from out west have a 7mm Mag, .300 Win Mag, etc. and don't want to buy a new rifle, then overkill away! My best advice would be to pick a rifle/caliber that you can shoot well and have confidence in, set it up right with good mounts on the optic and get familiar with how it shoots. If you sight any of the calibers I mentioned here 1.5 - 2" high at 100 yards, you can hold dead on a deer's vitals out to 200 yards, no problem. Good luck with whatever you choose!