It really depends on your budget. Your resource use is pretty reasonable and there are a ton of providers out there that would meet your needs. I would recommend going with an established host IMHO there is just less risk in doing so.
Since you need managed hosts I would point you to Knownhost, Wiredtree and Servint. All of these provide excellent service and support and I doubt they would have any problem helping you migrate your forums.
But you should take a look at the offers section and then do research for reviews here on anyone that catches your attention. I would then contact them directly with you needs.
My recommendation would be to get a VPS with 1 GB RAM or even more (Have you actually used a virtual server for this forums or you have been on shared account?). I would suggest you also to be careful with the different interpretations of the term "Managed VPS" because different company understands it in a very different way.
Otherwise no one would make suggestions here. You should spend some time to find out who are the VPS hosting providers that users define as reliable.