I've made handgun grips, and it isn't tough to do. I'd go with a wood that doesn't easily split, and I've used Walnut and Bocote and I made a couple that I can't remember what wood I used. Brazilian Bloodwood is a good looking (dark red with gold streaks) choice if you like red. The Bocote has an eyecatching look to it.
I use the old grips as a pattern. It can be hard to precisely locate and drill the hole for the crossbolt screw, so be careful with that. As for a finish, I've used mostly a handrubbed linseed oil finish and I've used a wiping varnish (Danish Oil or Antique Oil or something similar). You could use a varnish, but if you scratched it deeply, it would be hard to repair. The oil finish and wiping varnish finishes aren't too tough to repair. Probably a Tru-Oil finish, which I have not used, would also look good, depending on the wood you choose. Be aware that most oil finishes darken the wood somewhat.
One good thing about making handgun grips is that if you mess it up, you aren't tossing away much of a $ investment, so that takes some of the pressure off.