What advantage would a railed base give me? I'm pretty much planning on throwing the optic on it and keeping it that way forever.

Railed bases give you way more mounting flexibility in terms of ring placement and thus more flexibility when setting proper eye relief.

What kind of swivel rail adapter would you recommend? Would it be a good idea to get that instead of returning the bipod (in-case I want to mount something else on there, though I'm not sure what else you'd mount on what's essentially a hunting rifle)?

If you want to do it right, I'd just return it and get a proper sling-stud compatible model. Though if you didn't want to wait, you could get by with something like this, or like this.

Just wanna triple check as well: are you absolutely sure the mediums will fit? I don't wanna have another bipod situation and have to return them. I feel like a 50mm objective lens + scope caps is a bit bigger than the 'typical' scope, but I'm also not sure if the current scope bases + the medium rings will be more than enough to clear them. I don't want to overdo it cause I'd like it to be low, but I don't want to order them and have to do a return either, which might fuck up my weekend plans.

Mediums will be fine. You could go high rings but you will likely have to build up your cheek position to get proper sight picture. Weaver skeleton rings are perfectly serviceable rings. Burris Zees are also great. And now that I think of it, the Burris Singature Zees have inserts that you could use to gain your 20 MOA in lieu of a canted base.