The limit is only what your gmail (Google) account gives you.
In my case I have 2 gmail accounts each with 16 Gig Quota Limits- those are standard gmail accounts. You can have more space with gmail account by converting it to premium (pay for it).
Apple Mail limit is your disk space.
Folder limit is none (as many as you like)
If you right click on you gmail account in Apple mail and ask for Account information you will get the limit information you have with the gmail on they server. (not on your Mac).
It looks like this on my mac for one of the accounts:
To monitor what is slowing your Apple Mail down open the Activity under Window Tab in Mail. That one will show you exactly what is going on and who or what is slow.
The Activity window looks something like this:
Now to your Problem:
Gmail allows you to set limits for how many emails are transferred and synchronized each time you connect.
You can set the number of emails in gmail to speed things up.
I assume you do not need to have all 250000 emails synchronized each time.
Setting the limit will not delete the emails, they are still on your gmail account, the limit is for how many emails are transfered to your Apple Mail and you can set it from 1000 to 10000.
Here is how to:
Be aware that if you set it to "Do not limit the number..." that can lead to slowdown:
Finlay, I would say you do not need to start to deal with your own email server, simple adjustments to Google preferences can provide you with all your needs, but if you need to Google offers a high traffic business solutions as well.