The 85mm f/1.8 sounds like a good fit for those purposes.


The 70-200mm f/4L would be great for outdoor sports, but indoors f/4 is not going to cut it unless you can also rig the venue with a set of external flashes with wireless triggers. Even f/2.8 is about the narrowest you'd want to maintain reasonable shutter speeds needed for sports in the poor lighting of most gyms.


The f/4 zoom would be good for outdoor portraits (where you have room to back up a little but still be close enough for long focal length + close enough to subject to give you good isolation. The wider aperture of a prime allows you to do that from closer to the subject (and will give you shallower DoF in general).


The other often-discussed lens for these purposes is the 135mm f/2L. The issue there is that the longer focal length on a crop body means you're pretty far from the subject. With a 135L on a crop body, to get a full-body portrait of a 5'8" tall person (in portrait orientation), you'd need to be 35 feet from the subject. If you're only planning on tight shots or know you'll have a lot of room, the 135L is a good choice, but for portraits it's really more suited to a FF body. For shooting sports indoors, though, especially from the stands, the 135L is an excellent option.


A 3rd lens in this class is the 100mm f/2 - it's nearly a twin to the 85mm f/1.8 except for the 15mm and 1/3 stop difference, and thus a compromise between the 85mm f/1.8 and the 135mm f/2L (but closer to the 85mm in price).


Of those three - 85/1.8, 100/2, 135/2L - I'd still recommend the 85mm f/1.8. I loved mine when I had it, and took some portraits with my T1i that I really liked. I liked the focal length so much on the crop body that I replaced it with the 85mm f/1.2<span style="color: #ff0000;"]L II (a great lens, but optically the 85/1.8 is close, the non-L lens focuses faster which is a plus for sports, and it's 1/5 the cost). The 100mm is ok for portraits, but even the 85mm on a crop body is best for tighter portraits (you still need to be ~22 feet from a 5'8" subject for a full body portrait shot with the 85mm lens), but you can probably make that work outdoors. 100mm would be a little harder. The T2i has a lot of pixels to crop from, so that will help the 85mm on the courts/fields, but conversely, if your lens isn't wide enough, sometimes you just cannot back up.


Given the prices, you could get the 85mm f/1.8 (or the 50mm f/1.4) for your portraits the 70-200mm f/4L non-IS for outdoor sports and still be within (or nearly so) your current budget. [6]