Tri shorts are bike/swim shorts designed specifically for the uniqueness of triathlon. You wear it throughout as changing clothes in the transition area is a no-no. If you wear a wetsuit then this is just underneath. The extra padding in the seat area doesn't distract during the swim or run. It dries rather quickly. I did my first tri in a long Speedo and the rest in tri shorts...I REALLY recommend tri shorts.
You can get a top section of a wetsuit if you like rather than a full suit. But the full suits come off pretty easily so I would recommend getting one. Now sleeved or sleeveless is totally your call. I like the sleeveless because I like the full range of motion - although many of the newer sleeved wetsuits provide a great range of motion so I would throw that out. And, since you take your arms out way before you get to transition that doesn't play into additional time.
So, get what you feel comfortable with.
Fred