If your worried about washing a few pairs of knickers each week when added to your normal laundry load, your either going commando+ a little too often or your way too worried about the washing machine, seriously, max out at 7 pairs a week running daily if you can't wash more then once a week, thats like 1/8th of a washing machine load, nothing to worry about!
I wear stuff from Sports Direct, they have Puma briefs in which have a good stretch (eg don't suddenly sag and feel soaked halfway through a run) though are pricey for what they are I think its worth the extra. Gap also do great underware. I'd go with g-string/thong as oppose to full brief but mainly for the VPL! I used to find them uncomfortable to wear but actually its really easy to get used to them and now I put them on and don't really notice at all.
Worst types to wear? Full briefs, "seamless" stuff from M&S and infact any of the M&S undies, great for day to day use but just seem to soak up sweat otherwise, I end up binning them as a result! If your loaded enough get yourself a few pairs of the Nike range, I've had these in the past a long time ago, cost too much for what they are IMO but if I could afford it (and so justify it) I'd get myself new stuff from there but for now GAP and Sports Direct are fine.