I've used all of those methods for db's up to around 20 meg, after messing with settings, but I'm well out of practice with that stuff and would have to swot up again. Really it's best to skip the ACP and phpMyAdmin for larger db's. There are umpteen other ways you can do it.
![thumbs_up !*th_up*!](./images/smilies/ok.gif)
Moving the site shouldn't be a problem. Might want some tips on how you've set the site up and how the custom scripts work, but nothing major.
Might be able to get a cheaper package, but honestly I avoid like the plague anyone who offers "unlimited" storage and/or bandwidth for a few bucks a month. They're invariably oversellers, and won't give you anything like what they promise if you end up really needing it. They frequently also have terrible tech support. I'd rather pay for an extra carton of beer a year and have something solid.