What you want to use is a tool like
eMail Miner, basically it connects to your mailbox and pulls all the different email address out of it.
Then you take that list in CSV format and import it into
PhpList, which you have to download and install on your server, it's free. Or you can import the list into any mail campaign software.
With PHPList, you're going to have to set up your own mail server, you're going to encounter sending limits with GMAIL.
So if you have a VPS, it should come with Exim or Postfix (Both Free) and you'll need to configure and set the SMTP server in PHPList to use your postfix or exim account.
Then you should
inbox test your mail campaigns, a few places do this, basically, you get a seeded list of emails and you send to that list and it goes out and tells your placement. If you use the email miner, might as well use all the tools they have at that low price, you'll need all of them (Email Hygiene to make sure you got valid emails, Config Tester, Etc). It's like the email tool set equivalent of scrapebox.
Once you got it worked out, send the campaign - Just keep in mind a 1,000 emails is not a ton, but if it's targeted it can yield some results.