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.