One thing I love about Warcraft is the rich model graphics. I'm entirely unashamed to enjoy the dress-up dolls aspect of WoW. It's fun when you get new gear and your character looks different. A friend of mine from my old guild recently asked me how I go about putting together good looking outfits. He just got the Headless Horseman's Steed (congrats!) and wants to create a coordinated outfit to parade around with.
Honestly I don't have any great technique for clothes shopping, it's really not
very easy. Mostly I just browse wowhead's screenshots for things that look interesting and are easy to get. A good place to
start looking is either chest armor or helmets; they show up best in
screenshots. If you find one you like you can often find matching items
for other slots.
A good place to start on Wowhead is the 291 items sold by vendors that are not soulbound. Lots of lowbie gear here with distinctive looks. Another useful list is the 256 random enchant BoE green chests: you can generally find these cheaply on the AH and there's lots of interesting models. In general gear added to the game later (with higher item IDs) will look better; WoW's art is steadily improving.
Don't forget some slots are generally not visible: no need to find rings, necklaces, etc. If you're in a hurry then simply finding good shoes, pants, and chest will get you most of an outfit. Most outfits look fine without shoulders, belt, bracers, or cloak. Helmets and weapons are nice accents but you can do without.
Of course these snazzy outfits you patch together out of level 23 greens aren't going to help you when raiding. For raiding outfits you're limited to only two vanity options: shirts and tabards. Shirts are visible underneath armor, particularly the high level skimpy stuff. I usually go with basic white. And tabards are visible over armor and are great for hiding that ugly chest piece or mismatching pants. I also generally find that raiding outfits look best with the cloaks turned off.
One last trick: if you're bored and sitting in the auction house, do a search for armor you can wear and try on the cheap pieces in the AH frame. Sometimes you find something fun that way.