Any advice for my latest project?

I’m cleaning up an old Stanley bench plane from the 50’s. It has sentimental value though not $ value. I’ve cleaned up the metal work and squared and sharpened the blade, now I need to decide what to do with the handles.

As the paint was peeling off of them and had a nasty tendency to get lodged in my hands and under nails, I took some 220 grit sandpaper and some steel wool and sanded away the paint (red? maroon?) which left an interesting purple stain on the bare wood underneath that fades into the more blondish non-stained wood.

So, here’s my question. What should I do next to them? I want to finish the handles so I can protect the wood and ultimately use the plane again without rubbing off in my hands. Ideally, I’d like a nice thick glossy finish to show off the time its taken to get it working again.

I’ve been trying to get more into finishing some of my projects lately, so in the past couple weeks I’ve been buying a whole bunch of things that I’ve read about but have never used before.

So far my finishing shelf includes the following products: tung oil, danish oil, linseed oil, denatured alcohol, penatrol, brush cleaner, Cabot penetrating wood stain (colored amethyst – which looked dark purple on the test piece in Lowes but looks more girly lavendar when I put some on some scrap pine) and some Cabot gloss polurethane.

Any suggestions on what to put on and in what order?

Thanks for bearing with my rambling question and advice on my project.