robzilla - 4:13 pm on Apr 28, 2012 (gmt 0)
You can easily scale up on a VPS and if you choose the right provider you won't have to share your resources with others as you would on shared hosting. Around 256MB of RAM and a single core should be quite sufficient to get you started with either phpBB or MyBB. Install an opcode cache such as APC or XCache and go easy on the number of plug-ins and modules, use only what you really need. That way, a small VPS with the above specs can probably handle a couple thousand visitors per day -- and if it starts sweating, you can simply upgrade without a hassle.
As for phpBB vs. MyBB, I only have experience with phpBB, and I think it's great. I love the templating system, how it allows you to keep things simple (unlike vBulletin, for example), and so far it's had all the features I needed, and a solid community that produces add-ons and can provide support when required.