Can I register a domain name with a cheap registrar and transfer it to another hosting company? Pros and cons?

Yes you can. In fact, I would recommend the following: Find a web hosting company you would like and after you sign up they'll give you nameservers to set in your registrar. No need to transfer the domain after that. I did the same thing using http://www.GotHosting.org and they made it pretty seamless. After I signed up I got an auto email with all the information. Plus their rates were very competitive. On another note you could try Hostgator and be sure to use a coupon site like http://www.hostingdiscounted.com as they will give you a great discount initially.