Fun, isn't it!
I told you this is a journey, not a destination!
You never reach the end of the learning!
We used linseed oil for our rifle stocks in the Marine Corps. And, if it's good enough for a Marine's rifle, I think it will be good for your plane handles!
If you use the linseed oil just put it on in coats until the wood isn't having any more. You can put the wooden parts in a container add oil and turn them once in a while for a few hours. Then remove and wipe dry. I would give the handle and knob 24 hours or so before use. If you want shiny rub on layers of the linseed oil and rub until it gets warm!
You will develop a shine. I have seen rifle stocks that looked like glass. Wash your hands carefully after each coat!
Linseed oil used to be boiled so that it would polymerize. Now, they just put heavy metals in to catalyze the reaction. Don't
use the stuff for food contact surfaces (cutting boards, rolling pins, salad bowls.
LSO will make the wood look as good as almost any finish, give some protection from water (sweat) and is easily touched up. Just make sure any rags are spread out to dry. Wadded up, you may get spontaneous combustion! Whoosh, Bang, Nasty.
Actually no Bang, but a fire. Otherwise in an all-metal container with a tight metal lid. No plastic, this stuff can get hot!
Water-based Polyurethane will give a good appearance, but it is a film-forming finish and the beauty is skin deep. If it wears, and it will, you will need to sand and re-apply.