There are singlets and there are suits, they are not the same thing. A singlet is a looser piece of material and you could wear that for all 3 events. A suit is super tight and specifically designed for one lift, you would NOT wear a suit for either squats or deads when you bench. Suits don't give you any advtange when you bench so you should just wear a singlet. You still have to wear a T-shirt or a bench shirt when you bench, the T-shirt is optional in the deadlift.
I haven't lifted with gear in a while so I am not sure what the best deadlift suit is out there, Inzer makes good stuff and it is IPF legal. A lot of the stuff on Elite is not geared towards the USAPL so make sure it is legal if you get it. If I were you I would do my first meet raw just to get the feeling and my feet wet and then if you like it start experimenting with gear if you want to, although staying raw is cool too.
Good luck with the competition.