Don't want another singleshot 22, been there done that. PITA on a gopher field. I really liked the Varner I had, but, it was a PITA in the application, good bolt or straight pull action suits me better, with a big capacity mag.
Also have a 300Rook on an H&H sidelever action, that gun is fun, far easier to operate than a falling block or top lever, although , a Baikal underlever can definitely compete with it for ease of use. I'd be happy with either style of them in nearly all of the cartridges I currently have other guns in, if that was a little cheaper to buy than they are. And yet, a falling block is better to use off bags on a range than a break action.
As to cartridges, I have a 218Bee, no desire to change that, in a Stevens 044-1/2.
I have a 7-08 in a #1, it'll do the bulk of what needs doing for hunting, I might be just as happy with a 6.5 or 7x57R too.
I have a 30R Blaser, essentially a 7.62x68R, it'll do what needs doing for the bigger critters in N America and elsewhere, comtemplating buying a used 30-06 in an 1885 or #1 and rechambering the existing bbl one day.
I also have a 300H&H, in an 1885, it really is a sweety to shoot, but the 30R will do what it does.
For a big 5 gun, I'd go 450-400NE, 200-400gr loads in it, it is pretty versatile, but, I don''t need it, have to be a 10-12lb gun too, been there, done that one.
But, for a range gun, I'd like another 32-40 or maybe a 32RKS or Miller, in about a 12-15lb gun, it would be on a 44-1/2 Stevens.