Some people might use the lowest level of a server or even just shared hosting package. However, I think a larger server is needed, and that fact is true especially if more than one forum is being run. At the most, you would at least a package one step above the basic server package.
starting off should be as low as, then you update as you grow. Don't really want to spend to much for an small website. Unless you have way to much money to spend.
Do not go to the sites that say top 10 hosting or anything of the likes because those are affiliate sites and for them the best host will be the one that pays them the most for passing you on to them.
I would second @Empire on this one. I would prefer to start on the cheapest or the most basic package (even a shared plan or post2host plan) and then later move towards the higher plans if the traffic or any other parameters pose considerable challenge to the resources we signed up for.
but yet, I kept noticing numerous RAM issues. So I asked my host, I was like..."why do I have such little traffic, yet the 256mb guaranteed, 1GB burstable, isn't enough, that just doesn't make any sense?"
Best to start with Shared/Web hosting plan and only upgrade to VPS/Dedicated when needed. When using Shared/Web hosting look out for the ones who offer many resources such as CPU, memory and Disk IO as that will help your site(s) load much faster which is crucial nowadays for many different reasons.