I've worked with redwood in the past, and it seems like it would hold up well for the grips both from past experience and from some articles I've found.
In woodworking circles you'll generally be told to rely on hardwoods or fruitwoods where you want a tough, resilient handle for something.
Certain hardwoods and fruitwoods were the traditional picks for tool handles of all types for many centuries (and still are today in some cases) and for good reasons as they're strong, tough and generally resistant to splintering. Not that softwoods are necessarily weak, but comparatively they aren't in the same league for this sort of application.
While redwood might hold up well enough (it would depend on the piece to a certain extent) I'd be more inclined to go with a close-grained hardwood if possible. There are numerous possibilities but maple would be a good candidate among species that are relatively easy to get, especially if you're in North America, and beech would also make an excellent choice.
For the buttons and stick caps, I'm guessing that no wood I choose will be able to have the fine detail necessary while still maintaining the strength required, and that I'll need to instead make the structural portion out of metal or plastic, and add wood caps. Given that, at that point, fine detail is the main issue, I was thinking basswood.
Basswood is fairly soft to very soft (wood varies) so would be a very poor choice I think for something like this. You won't easily get it but a much better choice would be rosewood. Other dense, oily/resinous tropical hardwoods would also work well, but all tend to be expensive and some are no longer available commercially because trade in them has been banned due to over-logging at source.
You might consider instead using a resin-impregnated wood such as those sold for pen turners and as handle blanks for knifemakers.
I've never used a finish, since longevity was never really a concern. Having the feeling of wood is rather the point of the project, but from my research, that seems at odds with decent protection from wear/hand oils.
You don't need to protect from hand oils, they don't actually pose any risk to wood*.
Up to a certain point finishes don't protect wood from much in the way of wear. You'll get some protection from minor scrapes and gentler hits that would otherwise result in a ding or small dent, but in general the finish gives when the wood gives from an impact so really what finish is doing in general is protecting the appearance of a piece, not so much protecting from wear outright.
If you go with a tight-grained hard wood for the handles you could easily go without a finish, just sand to a fine surface and use it immediately. If you would prefer to finish then there are many alternatives, from oiling using a straight oil (e.g. BLO) or a penetrating finish (e.g. "Danish oil" or "tung oil finish") through to shellac or varnish. All of these options are used by someone out there to finish their tool handles, and each user likes how the wood looks and feels, and how it wears over time.
*In fact handling and the inevitable buildup of skin oils etc. in the surface are one of the traditional ways that some things were finished, this is sometimes referred to as "hand finish".