I have no idea what happens when you go over your limit with a gmail account, but I would defn' look into somehow pulling some of your old stuff (if not all of it) off of gmail and archiving it in some way.
I use ^ the same method here. Gmail with own domain. I use gmail desktop app, plus I use TB to download all sent and received msgs. You should always have a local copy of all your gmail. I had around 4gb... yes, downloaded them all. Took a couple of days but well worth it, and yep, it gets backed up every day too. If google ever has issues, I can still access all my messages. If my computer has issues, I can take my backup to my laptop and access on TB there...
So then do you have to buy your own server?...Right now I have almost 8 gigs, 31,500 messages on gmail....
You don't need to buy your own server. You just set up TB/gmail to download all your gmail messages. To make mine more manageable, I split up into 2 folders (one for each year as I've only been using gmail for 2 years). I recall having problems when trying to download the whole 2 years for some reason.