Chainsaw oil. Regular and often is all it needs. Keep a small stock of old clothes that are going to be thrown out and use them as your rags. Chainsaw oil at £1 a litre means you can do it often, but even then you don't need much.
For years I used automatic oilers (scottoiler) on motorcycle chains. By dripping a very small amount of oil onto the chain each ride it worked far better than just spraying thick lube/wax/teflon gunk/etc on it every 300 miles. The chains lasted measurably longer, although the back wheel always got a little muckier.
Mickleing your chain is a manual version of this, only you're keeping it reasonably dry as well not leaving a load of oil on to fling off. I wouldn't bother using a solvent at all.