There have been a few recent threads on this on the Triathlon Team here on Spark (see my page to find the team) but here is my opinion: Buy tri shorts!
Tri shorts have lighter padding than cycling shorts, but are designed to be worn in the swim, dry quickly as you get on the bike, and be worn on the run without feeling like you are wearing diapers. I love mine, and even wear them for some of my bike rides beyond multisport.
For the top, I now have a sports bra type tri top, but for my first tri, I just wore a black sports bra.(I knew it was going to get wet!) Many people prefer the one piece tri suit, but that wasn't for me--I get more use out of single pieces. I also did not want to wear a regular swim suit, because I didn't want to cycle with the suit's leg bands--I knew I'd be too uncomfortable on the bike.
After the swim, in T1 (the first transition), I put on my cycling shirt because I was a little self concious, and left it on through the rest of the race.
So the best advice is to wear one basic outfit for all three legs of the race. You can't change in transistion areas (it's completely out in the open). Add a shirt if it makes you feel more comfortable, but keep even minor changes to a minimum.
Here's one of the Triathlon team thread links:www.sparkpeople.com/myspark/team_messagebo
As for where to buy clothes: Performance and Nashbar are great choices. Other places to search to tri clothing are REI, Title 9, Danskin, and Team Estrogen. Or just search "triathlon clothing". And don't forget to check at your LBS to see if they carry tri clothes--mine does. This way, you can actually try the clothes on!
And if you tell me more about your race (like distance, location and tempuratures), I might be able to give you a little more insight.