Unknown 50s/60s track bicycle

Have you tried cleaning up the original cranks? They're beautiful! I'm sure they're not particularly lightweight but it's got to be worth a shot, right? Try the ol' vinegar and aluminium foil trick. Same goes for the stem and headset.

I haven't tried anything yet. The crank arms are really rusty on the inside. I'm going to check if the chainwheel can be removed, and then I should be able to clean them. Keeping the original cranks would save me from a lot of hassle, and they are indeed beautiful.

The thing is, however, I would prefer not removing the cranks to clean them. I have zero experience with those cluttered cranks..

The stem is no problem, I have multiples of those old Titans laying around here.

Option 1 with as many of the original bits as possible, I personally wouldn't even paint, just linseed oil.

Kurust/linseed, chrome polish, elbow grease, S/H rear wheel, front brake: nice bike.

I didn't know about Kurust or anything like it, looks great! I'm going to check my local shop for a product like that (I'm located in Belgium).

Here's a question: the bottom of the bottom bracket is really rusty, there's no paint left there. Can I use a steel brush to get most of the rust away (and get a smooth surface) and use Kurust after that?

Do not paint this, honestly don't. Most of the stuff with a clean and polish will come up nicely. Maybe rebuild the wheels if they are particularly rusty.

The wheels are 70s I think, and not so nice. The front hub is really rusty, and the rear wheel doesn't have a hub for a fixed cog. So I am on the lookout for a vintage wheelset (Mavic or something in the likes) with a fixed rear hub (brand doesn't really mather, just nothing too new).

Option 1, no question...
Whereabouts are you, I might have some 50's tubs you could use?

Option 1 it is!
I'm located in Belgium though.. I won't really look for vintage tubs, just regulars with a gum wall tire will be great. I still want to ride the thing :-)

I think you have your answer. No more puppy killings.

Yes, I have my answer. The hunt for a vintage wheelset with fixed rear hub is opened.

Thanks for the input everyone!