Melissa,
Runners and athletes come in all shapes and sizes. You should NOT wait until you lose more weight. If you feel you are ready for the challenge, then I say, "Get out there and do it!"
I am a runner, not a triathlete, and while I have never struggled with weight, I stand on the sidelines at Tri's (watching my husband) and marvel at the sizes and shapes going by. You should wear whatever you feel comfortable in. My husband, who is a runner who happens to do tri's, feels the most comfortable in his running shorts - so that's what he wears. He puts a wet suit over them for the swim (he needs all the boyancy he can get), but just wears his shosrts and racing jersy for the next two legs. Do not feel you need to wear certain clothes and can't compete until you can. He's an awesome athlete and could never fit into one of those one-piece wonders. He's too tall and skinny. He sure does pass a lot of people - especially on the run - who are wearing the "preferred" outfits.
Most running/biking clothes have a ton of stretch. If you invest in some now, they'll probably still fit while you continue to lose. The only thing I wouldn't buy until you are sure of the size is a wet suit - too big a financial investment - but there are tons of people doing tri's without them. Our sons occasionally race with their dad, and neither of them has a wet suit.
The only other advice I'd give as a runner is don't make the mistake of wearing cotton. It will chafe. It will hold the sweat and weigh you down and it will make you cold on cooler days. Invest in a top and bottom in a high tech fabric. You will be glad you did. Also - spend as much as you have to on a good running bra. You can swim/bike/run in it and it will be worth every penny you spend. Finally, don't scrimp on your running shoes. They will keep you healthy by helping you avoid injury which will be cheaper in the long run.
Bottom line - wear what you want, sign up when you want, as long as you are having fun there are no rules about any of that.
Good luck, God bless, and keep us posted.