First Triathong

I think people are picking on your thread title...

What do you already have?  

Assuming your first isn't an iron distance race, expect to not have a place to change so you'll swim-bike-run in the same thing and what you choose may depend on distance, weather, comfort, and budget.  

Many people use a tri-suit (1 piece) or tri-shorts and a tri-top.  These are designed to be body-hugging (good for the swim), dry quickly, have a little padding for cycling (specifically designed to not absorb much water, and not too much to affect running), etc.  I haven't shopped around, but you can get shorts for $30-50 and trisuits for $50-80.  I suspect from your username, you'll want a top if you get tri-shorts.  Of course, you can also spend a lot more...

I assume you already have a swimsuit.  If so, I suggest you try riding and running in it.  You can pull on shorts and a top for either if you're too modest to do these in just the swimsuit (and if this is the case, you'll have to jettison some modesty with the tri-suit as well...)  If riding in the swimsuit doesn't cause binding (uncomfortable even under shorts), try running in it.  Does it offer enough support?  If you can swim-bike-run in your swimsuit, you don't *need* to buy anything else.  Try running in a wet swimsuit, because it may be different than running in a dry one.  

Again, without knowing anything more about you, you'll have the same unknowns with a tri-suit that I've laid out for your swimsuit.  Does it offer enough support to run?  Does it bind?  Unfortunately, you won't know either of these until you've bought one that doesn't-quite-work...

You can pull on shorts and a shirt over your swimsuit for warmth or modesty.  Pulling either on while you're wet will be difficult, but you aren't going to lose your livelihood taking 30 seconds.  If your race is likely to be cool (you said March), you may want to dry completely off and put on some wind-resistant top.  There's a big difference between riding in 55F weather and riding WET in 55F weather.  My first race with a tri-suit was 60-65F at the start.  The first half of the ride dried out my tri-suit, the second half was me trying to warm up from the cooling evaporation.  

Best of luck training and racing.  

You can go absolutely crazy spending money on this sport.  My suggestion since this is your first, is to go minimalist and not spend a lot of money.  That is of course assuming you haven't already been bitten by the bug and opened your bank account to the triathlon gods.  You can just throw biking shorts, and running shorts on over your swimsuit for those portions of the race.  So just your swimsuit/googles/cap for the swim, bike shorts/top for the bike, and run shorts/top for the run.  Of course this is assuming that your swimsuit provides you sufficient support for your boobs during a run.  If it doesn't, I'm sure you know the trick that my wife still amazes me with of putting on/taking off a bra underneath a t-shirt.  If you don't like the sound of that a simple tri suit is a minimal investment and will cover you for all three stages without having to change.

Just enjoy your first race and have fun.  If you become addicted, then you can go nuts buying every bit of equipment/clothing/accessory you can imagine to help you with the sport.  I can't begin to tell you how much money I've spent on stuff that hopefully improves my raceday.