A possibly safe approach...
I suggest something along the lines of what is known as "paper dolling" in the MMORPG arena where your players can select the colours of the uniforms (and provide them with RGB knobs so they can get the exact colour they want), broken down to:
- Shirt colour
- Background (the cloth colour)
- Foreground (the player number)
- Short colour
- Sock colours (left and right could be different colours)
- Shoe colours (black, brown, grey, and white should be enough selection for this part)
Also, start out with a randomly selected colour combination (and indicate that it was randomly selected), then provide the player with an option to randomly select a colour for each item (right next to all the RGB knobs).
I believe this solution will provide you with the most unbiased approach possible, without violating any specific colour schemes (getting feedback from a properly qualified lawyer would be wise here though anyway), but also without limiting your players from selecting the colours of their favourite teams.
You could even provide them with an option to supply art to use as a logo, and then you wouldn't be providing the logos. Your game's user interface could even remember the 25 most recent paths to logo files (along with the colours) that players used so they can easily re-create their teams the next time they play.
Dealing with logos...
If you wish to place a particular logo on the shirts, then you'll definitely need to get permission from whoever owns the trademarks before including them with your game.
If you're good at writing letters, draft up a friendly one on your own first and then have a lawyer with experience in Intellectual Property to review it before you send it (don't be surprised if you are expected to pay royalties, as it is important not to lose the perspective that sports teams are businesses that provide a product in the ever-so-popular "entertainment" category).
Any correspondence you have with owners of the logos, for which it is safe to assume that they're all Registered Trademarks, should be done with the assistance of a properly qualified lawyer.