I know that everyones' selections are a little bit different to each other, but I would recommend:
Helly Hansen Lifa undershirts. Hardwearing, comfortable, and do their job come rain or shine. They also wash and dry in seconds, which fits your requirements.
I like to wear full leggings rather than underwear, it eradicates uncomfortable seams, and stops linings sticking to clammy or sweaty skin. The ones I'm using now are by EDZ, but there are loads of different ones out there for very little cash.
Link to some EDZ stuff - http://www.hideout-leather.co.uk/tag/edz/ . I don't normally go for advert speak, but they are as good as their promise 'keeps you warm in winter, cool in summer.' For 20 squid for the leggings, I think it is a bargain.
Brit army issue long johns are not as good, but still relatively comfortable (bit warm though,) for the bargain price of £3.99 on ebay.
I do believe someone recently (Grant?) recommended some underwear that he has been wearing but I can't remember where the thread was. If I have remembered correctly though, he couldn't speak highly enough of 'Brand X' underwear.
Happy Riding
Joel
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