Jesse, I'll dive into my experience to let you determine what would be best:
I found my current plane sitting in a hangar only an hour's drive away from me. Owner lost his medical but had still been flying it around the patch. It was out of annual by 2 years. The engine is at TBO, tanks were leaking. I bought it for $16k, and about 12 months later (that's not a typo), I finally flew it for the first time. My first annual was $11,000 and some change. I'm $26k into it and it's got a timed out engine and crap panel, but still is a hoot to fly. I've been lucky with the Lycoming's having the cam up top, mine hasn't been showing any signs of wear. Oil filters have been spotless.
With that said, you have highlighted the BIG possibilities. The engine can be considered a run-out. You can do what my friend Cody did and buy an engine off Barnstormers and swap it. You might be able to find a mid-time IO-360 for anywhere between $10k-20k and do a swap, instantly raises the value. The tanks, that's another big part. If you do bladders, it's a buy once, cry once deal. Half of the price of my 11k annual was labor in stripping and resealing the tanks alone, so I spent 5k on those alone.
I will say, when I saw the first picture, I was like "oh wow cool" and when I scrolled down and saw how bright she shone, my heart skipped a beat. That is ONE SEXY 201! Right now inside me is screaming "get it! get it! get it!" BUT you also want to make sure you are ready for this leap. Airplanes, especially at our age (I bought mine at 24, I'm 26 now) is A MASSIVE FINANCIAL BURDEN. I'm spending close to 90% of my disposable income alone to be able to say I own a plane. My girlfriend wants to go house shopping, but we can't because of the airplane. My truck is 20 years old and I would like something newer and more economical, but I can't because of the airplane. There are times that I have been depressed due to financial strain and my short and long term goals with owning versus not owning it.
If I had to do it all over again, honestly, hand on heart, I would go back in time to tell my past self to walk away. I'm not sure how your income situation is, but my plane is literally eating me out of house and home. I want to finish my IFR and commercial tickets and I'll eventually sell it, at a massive loss. And this is with a carburated, Johnson-bar C model. With the J, you've got the angle valve cylinders which are almost twice the price of their parallel valve brethren, you've got fuel servos, electric gear, etc.
You ask how much we think its worth and how much you would need? Well as above, someone said 50k for a runout and 100k for a perfect J model. But, that is a 1981 model and it was last flown in 89? Its a time capsule. I can't imagine it having much time, and being hangared is a good sign. I haven no idea what it would be worth but I would easily say you need $20,000 to get it back in proper shape, and thats assuming the engine does not need a swap.
But please keep in mind this is just my take! This is just something I wish I would have known when I saw my plane, because I fell in love. (A couple of the MS'ers on here also persuaded me not to undertake this project). It's not a smart move to fall in love with your first. and that plane deserves a home and if you have the financial backing and an A&P who is willing to help, it CAN be done. It just takes a lot of money