1) Mothers Mag & Aluminum Polish: for polishing metal, self explanatory. I've also used Flitz which works fine, but I find the consistency of Mother's easier to work with. Obviously, you should only use this on nickel plating. For gold, I simply use Windex (WITH ammonia). You can also use plain ammonia, but I think the Windex does a better job cleaning dirt, plus it smells better.
2) New Life: I will have to disagree with Peter on this one. Everyone I have suggested this to loves it and has not gone back to GoJo. New Life is made for wood, GoJo is made for skin. Yes, they are very similar, but New Life just works better on wood. It lifts more dirt, re-introduces some oils back to the wood, and is gentler on finishes. I don't know what their religious persuasions are, and frankly don't care. To use this stuff, you wipe it on, leave it for a few minutes, and wipe it off. Repeat until it comes off white. I like to do one panel or section at a time. When you are done, the finish will be tacky. This is normal. I always let the machine dry for at least a couple of weeks before proceeding with my next step.
3) Howard Feed-N-Wax: I like to apply this once the finish has re-set from the New Life treatment. Just 1 coat should be sufficient for most cases. After I let it sit for an hour or so, I wipe the excess off with clean cloths until it stops coming off. Again, I will let this dry for a few weeks before proceeding to the next step.
4) Renaissance Wax: This stuff was developed in the British Museum Research Laboratory and they coat just about everything with it from metal to wood to paintings. If it's good enough for priceless artifacts, it's good enough for my humble collection. Just apply a small amount to a clean soft cloth and do a light coat on 1 section of the machine, then using another clean soft cloth, buff it until it comes to a shine (it's a satin shine, not glossy). This will create a barrier and keep the wood from drying out and keep dirt out. Once you finish this, you'll only need to use a dry duster for years to come.
NOTE: if you have a badly alligatored mahogany finish, you will want to skip the wax, as it won't really improve it much, and may even highlight the cracks.
5) Oil: I use Hoppes No. 9 synthetic gun oil on fast spinning gears, bearings, governor, pads, etc. It doesn't break down or become gummy like other oils. I find myself oiling my machines less after switching to this. Avoid 3-in-1 at all costs, and don't even think about touching WD-40.
6) Grease: Currently I'm still using the same can of Lubrimatic high-temp wheel bearing grease (blue) that I've had for years. If I were in the market, I'd also consider Mobil 1 Synthetic (red). I use this on springs, slow-spinning gears, worm, ratchet pawl, etc.
Everything mentioned is available on Amazon if you can't find it locally, except new life which must be ordered from the manufacturer. They ship quickly, though.