Why not use that transfer as an excuse to delete old email? I try to limit my accounts to hundreds of MBs, despite having far more capacity. Reduce the weight you carry around rather than hire a bigger backpack.
At work I've discovered outlook has an expires after tag that I can set on each email - I set this on everything I save which keeps my saved messages clean. I haven't found a convent way to do that with anything else though I understand something like it exists.