Hi, and welcome to the wonderful world of triathlon!
Depending on the length of the race, there are a number of things you can wear. If you need to wear a wetsuit because of water temp, then I would see first if you can borrow one from someone you know, or rent one from a local shop. If all else fails, I ordered both of my wetsuits on e-bay and they've luckily fit (I checked out the manufacturs sites for sizing first) and they were VERY cheap- one for $20 the other for $40.
Diving biker hit the nail on the head. You could wear your sports bra and some tri specific bike shorts for the swim (the chamois is thinner and dries out quickly- regular bike shorts will get soaked like a diaper and be very uncomfortable). In T1, you can put on a shirt and wear that for the bike and run portion.
There are lots of options, and if you want to wear your swimsuit, you could always wear your sports bra under your swimsuit, then put your shorts on to bike in and run in the same outfit. The less you change clothes the better you'll do. You'll spend less time in transition and your body won't be starting and stopping so much in between legs.
And, yes, the goggles you wear in the pool will be good for the swim. The only thing that might be good is if the swim is into the sun, tinted goggles really help reduce the glare on the water as you look up to sight.
Which event are you thinking about doing?
Good luck to you!!