If you're going to be shooting portraits with strobes, I think you would be wiser to invest in the lighting gear at this time, and wait until later to get the faster aperture lens.
For most studio portrait shooting you will probably be using a smaller aperture somewhere between f/5.6 and f11. At those apertures, the kit lens should be sharp enough for now. If you've never done studio shooting before, you'll spend a lot of time perfecting your technique and you don't need to be distracted too much by pixel peeping for extreme sharpness. I guess if you wanted to get really creative you might use a large aperture, but if that 's your intention then you would probably be fine with some hot lights.
By the way, I think that the Tamron 28-75mm mentioned above is a wonderful lens for using in the studio. That's what I mostly use in my home studio, and it's extremely sharp. I actually find myself using the zoom quite a bit, so I don't think I would usually want a prime. If I have some time when I get home tonight, I might post some samples with that lens in my studio.
I don't really understand the school of thought that dismisses autofocus as unnecessary. I use the single autofocus point in the center, and the Tamron pretty much always focuses exactly where I want in the studio. Why would I want to bother with a manual focus lens, when the Tamron can do it without a thought in a fraction of a second? Just because you're shooting in a studio, doesn't mean the situation is necesarrily "controlled". Just try shooting my 2-year-old sometime and tell me how "controlled" the session is.
When I'm shooting little kids, I want to be able to shoot very quickly, because their patience can run out quick, and you have to be fast to catch that perfect smile.