I used lint-free cloths when I had a go at applying TruOil and that seemed OK. Disposable foam brushes might be worth a go, but my feeling is that with cheap ones, the foam can break up after a while. I haven't tried looking for more expensive ones, but you could probably clean them up with turps or keep them in a jar of turps between uses.

I've tried foam brushes and foam make-up pads with the Solarez. I don't think one is particuarly better than the other. You don't need much of the Solarez at all to coat a guitar once, so don't be tempted to get big foam brushes or pads and soak up a lot of the lacquer with them as you'll waste a lot. But keep it and the brush or pad out of any UV light and it will stay fresh, so it doesn't need clearing up. I had about 1cm of Solarez in the bottom of a small glass jar (an old spice jar) and that cured very quickly (and rock solid) in the sun. It also got very hot when curing that amount, so be careful if you do the same or it could crack the glass.