Based on your criteria, sounds like an excellent idea.
Sig-Sauer pistols have a reputation for shooting straight and working pretty much every time; they're a favourite with LEOs. They're also not usually overpriced and I saw quite a few available secondhand and in good condition when I was over at giftmas.
Ubiquitous in the USA (and useful as a step up from .22 LR) really means 9 mm Parabellum or .45 ACP. You probably cannot go wrong with either although 9 mm will likely be an easier transition, has a huge range of variably priced ammunition in a lot of different loads. I have to say that in pure ballistic performance for self-defence, the .45 ACP is probably better but shot placement matters much more and you should easily become accurate with 9 mm and some practice. If you're looking for flexible purpose gun that you can shoot at the range and realistically hope to defend yourself with as well and not break the bank, I think you've settled on a good choice.