What I've heard both from friends and relatives who are serving and just from the forums is that folders are generally OK everywhere, and I haven't heard about any regulations about what brands. I also haven't heard about any length requirements, but I would think that you would want to make sure the knife is legal in the state the base is in incase you want to carry your knife while off base. Granted an LEO isn't likely to hassle an active duty service member, but why take the chance.
I know that the PX usually has a variety of manufacturer's knives for sale. I haven't heard of any requirements of brands for knives, and I know several of our own custom makers have knives in Iraq and Afghanistan right now.
Fixed blades are ok when deployed and may be ok while on base/stateside depending on local command.
One of my cousins had a multi-tool issued to him when he got to Iraq. You can't bring knives to basic training anyway, and you're probably safe with a folder in the 3" range, so why not just buy something like that before you can figure out the rules, which I have a feeling your recruiter won't be able to give you a clear answer on as they vary by command. Wait to buy a fixed blade before you know what you can have, and I would even say hold off on a multi tool as you may be issued one.