Welcome to tris!
If you're not super blessed on top, then running in a swimsuit would be just fine! I've seen people racing the whole thing in just a regular one piece swimsuit with running shorts thrown on for the bike portion. If you are super blessed on top (unfortunately I am), you might just want to try a bra underneath the top. Just make sure to try it out in practice a few times to make sure you won't chafe. Swim in it, then run to see if you'll have any chafing issues.
You'll not be surprised at all the various types of clothing you'll see at a tri. For my last race I wanted a new tri top, but didn't want to spend $50, so I just bought a compression type tank top (same type of material as a tri top) for around $15 at Target, and it worked great. In fact, I've been using it a lot latey. Wear whatever is comfy and works well for you. Just make sure you use tri specific shorts. The thinner/quicker drying chamois will make your life very pleasant (and they're meant to be used for all three disciplines).