If it's an Avocet Touring seat, it's original. Can't blame you for not wanting to sell, but I had to ask. The last thing I need is another bike. But that would be the one to have!
Personally, it's a work of art, and should be treated so. I would keep it spotless and enjoy it for local, casual, nice day riding. It would never see the dirt. That's how I treat my '85 SJ.
I would recommend the Specialized Hemishphere tires. They give a nice smooth ride and have flat protection built in. It can't hurt to replace the cables, and it's cheap. The brake cables are bigger than the standard brake cables, so if you replace them, make sure you get the right ones. I would clean every inch of it and use car wax on it too. You have a real peice of mountain bike history, don't treat it likes it's just another bike to ride. 25 years from now, the 2011 Stumpjumper will just be an old, out dated bike, that '83 is a classic right now! You never see them for sale, and when you do, they're all banged up. There's always an old Sport version on Ebay, but never the original Stumpjumper. The only other thing I would do would be replace the bar and stem you have for a Bullmoose bar. That is to me what really represents the vintage Stumpjumpers. It would be correct for your bike too. Specialized would use what was available for parts at the time and make changes when they had to, and that caused certain variations each year. Both my '83 and '84 had the Bullmoose bars. They show up on Ebay from time to time. Just make sure you get one that has the cable hangar on it.
I love your bike, and I hope you do too. If you have any questions about it, just ask.