Just to give you an answer on the miter saw if/when you go that route, a 10" saw should be more than sufficient for minor home repairs like this and small to medium woodworking projects. If the 12" was a viable option budget-wise, I'd say better to use that extra instead on a basic folding miter saw stand, a quality blade or two, that sort of thing.

I mean it's a tradeoff, right? And only you know what kind of work you're aiming to be able to handle in the near future. A 12" can handle wider and thicker stock, and when that's what you're working with (like if you're cutting 2x6's for some framing work or something) then it's great, and the extra weight is an afterthought for the tool that does what you need it to do. But from what you're describing, I'd say a better quality 10", a stand, and a good blade or two should serve you very well for awhile.