White panties - Fairly neutral. This might be what's used as a basic if it's not really a fanservice show or something, but if you're seeing panties it probably is a fanservice show.
Black panties - Elegant and sexual. This color tends to be more seductive than white. Especially as I'm thinking of lacy pairs...
Red panties - Not a fan of red in general.
Other color panties - Not as common as White or Black, but sometimes it's necessary to have variety. I like anything except Red/pinks (excluding flesh-colored, I suppose) and Yellows.
Printed panties - Not really big on animal print panties. Paw-print might be cute (though that might fall under "polkadot"). Other simple designs might work well too. Also, this makes me think of strawberries for some reason...
Side-tied panties - Easiest to remove so certain characters *coughYuecough* look good in them. I'm not big on it otherwise, though it works better as swimwear (so that the knots don't rub on pants/skirts).
Striped panties - Classic deliciousness, as Zettai and others have agreed. Though of course it has to be horizontal as people say that vertical stripes are slimming and butts look good when they're squeezable.
Polkadot panties - Eh. It's not common for a reason, but it probably works on younger "loli" girls as opposed to mature ones.
Backless panties - If it's just a part of the crack/butt that is showing (such as Sakuya from Koharu Biyori; Sorry, but I can't seem to find a good image of her butt) then I REALLY like it. However, true backless (a la loincloth) is horrible. That leads to censors removing perfectly good buttshots due to other "parts" being seen. Go butt-holes, I suppose.
Spats - Skin-tight shorts basically. Nice for a sporty/tomboyish type I suppose, but I really don't see them as being "underwear". I guess I don't quite see the appeal in girls wearing spats under clothes. althoughNope, no appeal.
Bloomers - Poofy underpants. Elegant, but it often hides the butt and might even cover part of the thighs. That of course ruins what underpants is supposed to do xD.
-Notice: I completely forgot that gym uniform bottoms are called bloomers as well. I do really enjoy those type of bloomers, but like with spats I see them more as "outerwear" than underwear.
Thongs - Sexually probably my favorite (outside of the partial-backless ones). You get to see every bit of their cheeks and as a bonus the anus is likely covered. Though this might run into the ""That" is showing and thus look "convenient" light appears!" problem that plagues anime these days.
G-Strings - See thongs's main problem, only worse because the problem WILL BE there. I really dislike G-strings as they seem uncomfortable as well.
Fundoshi - Nope. Hate it with all of my hate. Basically it's like a G-string or thong in concept. Only instead of a thin piece of fabric there's a folded sheet that's twisted and tied to look uncomfortable between a girl's buttcheeks. Either that, or it looks like a napkin with a band on the girl's waist. Really don't like fundoshi.
Other - unknown, I'll talk about any that I can think of:
-Swimsuits - It's not panties so it's not embarrassing! But while bikini's can fit the above bottom-wise one pieces have their benefits as well (especially with flatter girls and competition/school swimsuits).
-Sling outfits - If you think I like these after what I said about G-strings you're crazy. These are even worse as they make the breasts look unsupported. Though to be fair, it does show off the butt well, but it's like a girl took a G-string and pulled it up to their shoulders (even if that doesn't make sense material-wise). Overall, thongs are better.
- Nothing - Well, it does show off the butt which is really nice, but censors have a field day with and would probably censor the entire butt so there goes that moment until DVDs (hopefully). Plus it's not really practical, especially with a skirt.
-Bandage/Band Aid - Like nudity, but I suppose that censors are slightly more alright with it. Though I can only imagine what taking a bandaid off of "that" would feel like as taking one off normally is painful. I'm not good with females getting hurt for fashion.
-Leaf - Like Adam and Eve I suppose. Still, there's nothing to hold it on in most cases I can imagine. Leaf-like prints or underwear that's leaf-based (see Queen's Blade's Alleyne for an example) has the possibility to look good, but that's mainly due to it resembling a thong or something similar. Also, be aware of the plants used as poison ivy or something similar I'd assume would be painful.
Long story short: I picked Striped panties as not only are they common, but they look great on the widest array of girls while working well as "innocent" fanservice.
TheUnexpectedFan said: It causes me mental distress to pick. I am saying all of the above.
You could always do what I did and describe why you like/dislike each pair or something. Though that would be far longer than you'd probably want it to be.