I agree w/Henry. From the sounds of it, you have a real nice spiral staircase. ANd if you're lucky, the wood is already oak. If not, beings you have spirals, it would be best left to a pro.
What I suggest you do in addition to what Henry said is to have a pro or 3 come in an estimate the job. FIRST, find out if you have oak. (ASK all 3 contractors.) Then, ask them what it would cost to refinish the stairs. THEN, ask them if you can save any $$$ by doing anything yourself. (ONLY ask this questions AFTER you've gotten your estimate. Let the pro estimate what he thinks needs to be done, then you ask about what you can do to cut the cost.) For example, he may say you can 'strip' the balusters and sand them down. (Ask what/how you should do that, depending on what you have now.) He may also say you can disassemble and reassemble 'stuff' (if there's anything of such nature.) ANd so on. Perhaps, you could do some of the 'finer sanding', like around the balusters and center-post too. ALL these little things add up to time and $$$! So don't hesitate to ask him these types of ?'s (AFTER you've gotten your estimate.)
To compliment what Henry said about using any type of laminate, I wouldn't for the same reasons. You won't be able to refinish them. DO talk to your contractor-of-choice about what could be done to minimize wear-and-tear on your newly finished stairs. IF you have hardwood above and below the stairs, 'runners' with rubberized bottoms are great for helping to pick up grit and such to prevent scratching. Obviously, if you use your stairs a lot, they will wear quickly from just walking (and sliding across them as you step.) I do suggest on many occasions that the homeowner use padded 'treds/mats' on each step to protect the finished tred. (This is what gets the most wear AND it will help with traction if you have children or wear socks a lot.) You only need them where you 'walk'. You don't need to carpet the entire stairs (because if you do, why refinish them?)
Well, anyways, 'nough said. My best to ya and hope this helps.