My old mate Andy had an Airsporter when we were kids, he went on to use it when he was a gamekeeper. It is an excellent tool.
He used to use a light oil, just gun oil out of a tin to lube the trigger and loading port mechanisms, all moving parts essentially. He was careful to wipe off the excess. He used to give the gun a wipe over with an old oily rag after each session, that was it for day to day maintenance.
We changed the spring once, we managed it but I would get a gunshop to do it if I had to do one again. Springs are readily available on the web and in shops. The only problem is that in fitting a new spring you may send the rifle over the legal limit. If you get a gun shop to do the work they can ensure the gun is legal when it is returned to you, thus no problems with the plod later!
As previously mentioned a new washer would be a sensible addition to the service.
Then why not sand the stock and treat it with either danish or linseed oil, re-blue the barrel if necessary. The rifle will be as good as new.
My shooting partner, Jon, has a BSA Super ten and BSA have been excellent in helping with his enquiries.
Best of luck.
Stewey.