Could you add detail about your motives?

Are you asking if it is "worth restoring" as an investment to sell/flip for profit? (the answer to this is no)

Are you asking if it is "worth restoring" for your own personal use? (Only you could answer this. You will likely not ever get your money back from any you put in.)

I'm not sure if it needs a bunch of work according to what the pictures show. I looks fairly easy fix stuff for someone with some mechanical skills.

I’m not trying to fix it to sell. I would like it play it. I would like to see it as it looked when it was made. I would like to know more of its history. Someone put time and love into this banjo and I would hate to just throw it away. Still, I have to be practical in how much I can spend on it.

are you familiar with the styles played on a tenor banjo? if so and thats what you're looking for , it probably wouldnt take too much money to get this playable. I wouldnt pay for a restoration, just get a setup and get it playable.

I’m very familiar with contra dance music but from what little information I’ve gathered, this banjo was probably intended for jazz. Don’t know if it works for the style I play. Not sure of the best way to tune it but I play some mandolin and guitar so I can adapt to various tunings and I am open to learning different music styles. Still, I am interested in the looks and craftsmanship of the instrument so I really would like it restored.

What work does it need? It looks fine to me. You could replace the head, but the old skin that's currently installed may have some life left. If it were mine, I'd simply install new strings, tighten up the head, and play it.

I wouldn't try to restore it to new condition. It's ~100 years old and should have a patina. Patinas don't affect playability.

Personally I wouldn't. To spend $$ getting it pristine like it came out of the factory would destroys its patina. Just get it playable. Just my 2c worth.

Polishing up the wood and metal and just a general cleaning will do wonders for it. It looks like the tailpiece may need replacing and the peghead veneer is broken off in places. I think I’d like to see what it would cost to replace that veneer while keeping the inlay or new inlay. There is a small tear in the head so it needs replacing too.

Don't polish the wood or metal - you'll damage both. The most you should do is clean the metal parts with dish soap and water.

You can play irish tenor banjo on it, that might be the closest to a contra dance style, but most contra dance music is old timey five string banjo. Like others have said, a light cleaning and good setup is probablly all this banjo needs. Dont refinish or polish metal on antique banjos.

Yup, looks fine to me. Not pretty but certainly functional. As John mentions, you could remove the hardware and scrub it with a toothbrush and some dish soap. Soaking in diluted vinegar can get rid of more stubborn corrosion, but this should be done sparingly. 

If you need to replace the head, keep in mind that a plastic head may not fit due to the rim being out of round (hard to tell from the picture). In this case, you'll need to mount a new natural head. Not difficult or expensive, but takes some preparation. 

It would probably be worth removing the tuning pegs and getting rid of any dust/gunk in or around the holes. Just use a damp rag. If the edges of the holes are in bad shape, you could try adding a leather or fiber washer. The tuning pegs themselves will need adjustment (via the little screw) to hold properly. 

Fixing the peghead veneer is a different level of service. I wouldn't mess with it unless the veneer is actively coming off, in which case you could put some glue into the exposed seams. 

Even if you don't plan on playing Irish music, you still might consider GDAE tuning when shopping for new strings. That way, you can directly transfer over whatever you know on mandolin. 

Vinegar of any dilution is a bad idea on nickel plated metal. Stick with dish soap or do nothing.