Yes, you can have both a traditional and a Roth. You can max them out
in total, based on your limits. And yes, you can convert. But this is not that simple and depends on different factors. So it'll be easier to direct you elsewhere and let you decide based on your own situation.
Fool.com: All About IRAs - Introduction
This is pretty comprehensive. If you want to jump straight to the limitations and about the converting part, to the right choose "What IS an IRA?" and Roth IRA Parts I & II.