How to pick the best modem/router?

I am wanting to buy my own wireless modem/router because I can save a lot of money if I don't have to rent one out. Also I can get a better one than the crappy ones they lease out. However, I heard that it works best if you have a separate modem and router than if you have one combined. Is this true? Also I think I want a pretty good modem/router even though I probably wont be using it to its full potential where I am currently living. This means I'm going to want a wireless N router which will allow me more speed and further range. The N router is the best for this right? Lastly I want something that will be compatible with most internet service providers. I have dealt with companies that connect the modem/router to a cable connection and others that have connected it to a phone line. Is there a modem/router that is compatible with both these connections? I want something I can easily use and be able to relocate with and change internet service providers when I need to. Any help will be greatly appreciated and points will be awarded. Thanks in advance.