The 18-55mm lens that comes with most T3i kits is most useful for introducing you to a DSLR, not so useful for taking great pictures. The only good pictures that I ever shot with mine were taken in bright sunlight.
DSLRs have a variety of lenses available because no one lens is ideal for any purpose. I would definitely look to replace that 18-55mm kit lens with something better before too long. Having a good wide angle zoom is invaluable. The single best thing about the 18-55mm kit lens is that it is small enough not to cast a shadow when you use the built-in flash.
Your camera works with either EF or EF-S lenses. With the exception of a wide angle lens, I would recommend only buying EF lenses. There are some pretty good EF-S lenses, out there to be had, though. Canon's best cameras cannot use EF-S lenses, just EF lenses. Deciding on what lens series you want to invest in is something to consider, if a camera upgrade could be in your future. I also think most EF lenses are generally better made than most EF-S lenses.
For your immediate question, I still think the EF 70-200mm f/4L lens will do a great job. But, it could be a little long [too much focal length] for many general shooting scenarios. The EF 85mm f/1.8 is a good lens for a full frame, but I think the EF 50mm f/1.4 may work better on your T3i, if paired with the 70-200mm f/4L. Even the EF 50mm f/1.8 STM would work with it. [A really good wide angle for a Rebel is the EF-S 10-22mm f/3.5-4.5 USM lens.]
But,, this still leaves the you with no replacement for the 18-55mm lens for now. Remember, most of the zoom lenses being suggested will not work with the built-in flash. They're too big. The flash doesn't raise up high enough to clear most lenses, just the shortest ones out there that have fairly narrow barrels.
--------------------------------------------------------
"The right mouse button is your friend."
