Emails +++

I have just bought a IMAC desktop, upgrading from an old PCI. I am 60 , IT skills just ok.
My mail account is working, however the bar at the bottom on the mailboxes informs me that over 300,000 emails are downloading. I have received about 1,500 .
I have set filters to delete junk mail etc but don't know what else to do to stop this. Any suggestions would be very welcome.
Many thanks.

Sounds like you're using Mail to check Gmail? What version of OS X are you running?
This is/was a known issue with early Mavericks.

I only bought this on Saturday, it just says OSx installed, I don't know what version. So,latest version maybe?
Many thanks for your help, I appreciate it. I don't know what to do though. Any suggestions?

Top left corner, click on the apple - select "About this Mac".
Window pops up, looks like this:

Oh, right, it's OSX 10.9.4
Processor 2.7 GHz intel core 15

More downloading this morning, but only 22 , not thousands thankfully.
Many thanks for all yoUr help.

There was a bug in early Mavericks which caused Mail to download ALL mail in Gmail's archive.
It was supposed to be fixed. Shouldn't happen anymore.