I've had the same problem with bumps and irritation in the past (sexy!), especially after shaving, so I definitely know what you mean. I'm SO particular about the underwear I buy!
First, I've found that for me, 100% cotton undies are better for skin comfort than any other fabrics, or blends. Plus, I don't want anything satin or lacy for everyday wear, and it seems sometimes like that's all there is!
Second, I always look for pairs on which the waistband isn't too "significant" - if it's a big bulky band, or of a different material than the rest of the panties, it tends to make for very annoying hip bulges, or roll down goofy when I sit.
Finally, what's most important me for avoiding irritation is that the leg holes be "wrapped" - that is to say, not just exposed elastic. For example, Fruit of the Loom's basic cotton undies (like this:
http://www.basicsportswear.com/newco...e%20ILD205.jpg) have leg holes that are basically just exposed elastic bands. Bad news on the irritation front!
I used to buy nothing but this one style of Gilligan & O'Malley 100% cotton hipsters from Target, but they stopped making them about a year ago so I'm forced to experiment.
I've had good luck with all of the following, however:
Hanes ComfortSoft Stretch Hipsters (about $10 for 3 pairs, Kohl's): http://t1.gstatic.com/images?q=tbn:A...53y4rncFRmcaqA
Jockey 100% cotton Elance Bikinis (about $20 for 3 pairs, Kohl's): http://t3.gstatic.com/images?q=tbn:A...J2yH6cr8ee9vEH
Gilligan & O'Malley Ultimate Modal Bikini (about $10 for 3 pairs, Target): http://t3.gstatic.com/images?q=tbn:A...mSP7LMvYzl6Xnw
Your mileage may vary, but those are my recommendations off the top of my head. I like fuller-coverage "hipster" type styles, but of course these are all available in bikini or brief, or sometimes boy-short if that's what you prefer. Those last ones, by Gilligan & O'Malley, are the closest thing to my old favorites - they're a blend but very comfy and are really good for avoiding panty lines. As a caveat, though, they don't hold up terribly well to repeated washing/drying. At $10 for 3, though, I guess I didn't expect much!