I think there are a lot of misunderstandings about Staph, Strep, and MRSA. MOst people will be quick to blame the mats at the gym or someone else but in reality, most of us have staph on us, in our armpits, in our noses, and some of us can become/are carriers that wont be affected by carrying it.
Problems arise when you epidermis becomes injured and the bacteria has time to settle into your wounds, even small abrasions like nail marks or gi burn. The best course of action is wash after training asap and clean your skin/wounds with hibiclens (a antibacterial) and put neosporin on your wound. Staph is a slowly developing infection and that sound be ample protection.
If a infection does arise, it doesnt always mean its staph, streptococcus (the main ingredient in strep throat) is an other common bacteria that can cause an infection, so the best possible course of action would be to get your infection cultured so the doctor can find the proper antibiotic.
I have had MRSA, Staph, and Miocci's Granuloma (the king of fungal infections) and have had some true horror stories of misdiagnoses and the effects it can cause..
Edit: Wash your gear in HOT water every time within an hour of training and if you do happen to have an infection, do like most people on this board have said and clean your sheets, towels, clothes etc...