With, as you say, only average math skills, I would advise that you use a library instead of trying to write your own physics that supports ragdolls. You're less likely to become very frustrated or completely stuck to the point of giving up. Not that I think you would, but physics isn't always easy or intuitive to implement. For ragdolls, even if you just have skeleton joints that are unconstrained ball joints (vs., say, hinge joints with rotation limits), implementing ragdolls requires somewhat advanced math. Then there is the issue of authoring ragdoll content...existing libraries do have art pipelines for creating these things, but if you roll your own you'd have to deal with the content development tools as well....lots of work that as a student of game development you could avoid and be none the worse for it.

If you use one of the open source physics libraries, such as Bullet, I'm sure the licensing is such that you could ship a commercial product without paying a license fee or royalty. I would, however, be very careful to read and comply with the license agreement for the library itself and the separate licenses that might apply to any dependencies. With open source, the issue of dependencies can be a legal pain, since different open source licenses have different requirements in terms of distribution. Commercial libraries may have less complex licensing (e.g., if they are self contained and don't use any external dependencies) but there may be license fees or royalties or other things that are troublesome for you. I don't mean to frighten you about legal stuff! Bottom line is if you intend to do anything in terms of commercial or even free public release, do your homework before you do so, to make sure you are legal.