What to use

If you have to take the varnish all off, Try a good stripper first.
That really does not look to bad, maybe just scuffing and re-applying the same varnish to re-freshen it.

There are some folk out there that use a clear coat of epoxy on the bare wood, then lay varnish over for U V protection.
The epoxy holds up from rough handling better and won't peel from the wood like just varnish.
In a project like yours, you could already have varnish over epoxy.

Like Ralph suggests, a light sanding then overcoat. If you sand through to bare wood, there will be a color difference, so consider how much it offends you when coated, because the only option is to get everything back to bare wood. Having a slightly darker "birthmark" in the finish is something most people don't notice, but can drive you crazy if you're that type of person. I'm more forgiving when looking at a project like that. I used to obsess over perfect and dust-free coats, until I learned that varnish surfaces can be wet-sanded and polished like any plastic. Sanding between coats removes too much applied material, so I scuff with a brown 3M Scotchbrite pad between cured coats. It's also possible to lay on "hot coats" relying only on chemical adhesion if the preceding coat is "green" and the weather is right.
An inexpensive way to preview what it will look like, you can Scotchbrite the whole thing, solvent-wash with paint thinner, and rattle-can with something like THIS. Cheapest way to get started with varnish, since the good stuff is $80+ for a quart. Sacrilege, I know. I've been down the Epifanes and Badger brush path, but ultimately, all varnish is temporary and requires maintenance.
If you want to keep that lovely honey-gold appearance, I would suggest Schooner Gold, especially since it builds faster, too.