It's kind of a tricky question with many different caveats. First off, I'm not a "pro". I have a FT job in a completely different field and stumbled into photography as a hobby about 6 years ago. To date, I haven't really put myself out there and tried to live off of the lens, but have thought about it very strongly at times. I've done several jobs, weddings, some seniors, some family and child portraits, etc. that have paid for all of my toys. I now have enough gear that I could feasibly open a studio from the jobs I've done but I am short on backgrounds etc. When I say gear, that includes redundant gear that you would need if you market yourself as a pro including multiple bodies, flashes, etc in the event that something fails. I think this is really a business that grows or fails due to word of mouth. If you have a good product, word of mouth will continue your business. Your ability to market yourself and function as a sales/business man/woman will continue or sink your business. You success as a business will depend 85-90% on your business skills and 10-15% on your photog skills.
Prints or CD? I've done both and really just prefer the CD route. If I were really in a FT business, I would do prints only probably, but doing it on the side, I just want to do the job, edit the work, deliver and move on. I really don't want a relationship with them which does limit your $ some as well as furthering your business. As for fees, there's a lot of different theories and you really need to just decide what works best for you. Some charge more up front and less on the back end, it's up to you. Another thing to consider is having someone to back you up in the event that you can't fulfill your obligations to the client. Consider a booked wedding and you are in an accident and can't make it to the venue. You're business could be failed overnight if you don't deliver and have someone to cover the event in your absence. It's things like that which are out of my control that has made me not pursue this as much as I'd like.
I guess that's a start to answering your question. It's a pretty broad question and others will weigh in as well.