unfortunately, the development of forum software (both paid and free) has been hitting a brick wall recently. there are many scripts that allow the transfer of databases (seamlessly? never done it myself) so your starting forum software shouldn't be too big of a concern for you.
i would suggest mybb for free software. there is a lot of plugins still in production/working in the current version. understanding the software isn't too difficult either as it's pretty straightforward. the software has been around for a long time, so even if you are struggling, there is a lot of information around the web.
there are some big boards that are still using (heavily edited) versions of mybb. if you have some skills, the "hacking" aspect of mybb is great too. maybe that's appealing to you?
i got to this point and reread your thread. i missed the point entirely haha. oh well, this will still be posted but i will post some information for you that is relevant.
some software (i believe) allows you to export (to some extent?) the information so if you struggled transferring to a paid host, with your free host, that will be an option to consider. you can pick up some cheap shared hosting with a cpanel, that will give you most user friendly approach - unless, of course, you know of linux then even better - CHEAPER than cpanel (in some cases). definitely keeps you more involved and you know your system is secure.