You can have a look at our dedicated
Hosting page where some hosts are selected that we know to have been very reputable long-term.
The point is mainly that we're not experts on hosting providers and the specific needs that your website with its specifications need. We are experts on the inner workings of the phpBB software. There are people that know much more about servers and how much load they can take (etc.) than most of us do.
What I can say that seeing as you're not planning to have a very high-traffic board, most reasonable hosts won't pose any problems. You talk about free hosts, that's something I wouldn't recommend as they quite often restrict you in the things you can do. You can review our
Requirements section for bare necessities.