In my experience so far Google groups is actually quite buggy. I was disappointed when I first started using it because I expected more from Google, I know its free but hey...So is phpBB.
Also the inclusion of the quoted text in every single reply unless you manually delete it all first out of the reply box is frankly idiotic. MANY people for years have made suggestions that this should be disabled somehow or an option to filter it? nope......
Anyway that's my moaning over with. It seems to make sense that with the small number of us at the moment we don't need a cavernous forum. For the most part I usually just click "view all topics" anyway to see if and what new stuff has appeared.
I tend to use this a more of a forum than a mailing list, Others may have different opinions to that, What you would want is a way to parse a header file in the email so you could sate something like <category>Electronics</category> and when you mail it off it would know that its supposed to be a new topic in that category, This may already be a poorly documented feature?
Personally I think Google groups is not ideal and the possibility of moving onto something like phpBB or similar could be a long term goal, setup is automatic, You just need a php parser and high level access to a database on any OS with a range of DB options (Would have to check there site for which exactly are supported)
(I have had phpBB running on my Raspberry PI with MySQL and php5 plus a couple of additional php librarys all straight from the raspian repo's with no messing about. All you have to do is give the setup script a username and password for the database and it sets it all up for you then deletes itself, leaving a fully working forum.