I've done alot of painting (I'm a sign painter...among other things) with foam brushes. They can really be a godsend, esp. with water based paints. Unfortunately, oil paints will not flow from foam.

I really like white china bristles for varnish work..they are expensive, but will last a very long time when cared for properly. You can keep the brush suspended in a can of mineral spirits during the duration of the painting job. That way you only have to clean the brush once.

'tween coat sanding can be light. It really helps to get a fairly uniform matte finish. this will make it easy to see the next coat as it is layed down.

I use a clean rag with a few drops of linseed oil for a tack cloth...I don't see any reason while mineral spirits won't work.

All to be taken with a grain of salt.

Good Luck!