Did progressive quote online $390. Same as my current coverage. Will I have to go back and forth between them to stay at the same rate?
No, that isn't how insurance pricing works. In six months your Progressive premium could shoot up and your GEICO premium could drop. Insurance companies are constantly adjusting their rates dependent on the overall payment of claims in your state, region, and/or zipcode. Sometimes they take rate increases, sometimes they take rate decreases. Even if your risk as a driver stays exactly the same, the activities of all the other drivers around you can and does impact your rates. They don't lower rates to try and get new customers in. If you wait 6 months and call Geico again, you are just as likely to be given a quote for a higher premium than a lower premium. There isn't any negotiation when it comes to insurance premiums. They are set by computers and rigidly applied.
Personally I wouldn't switch over $20 if I was happy with my current coverage. It would probably need to go up $50 or more for me to consider shopping around, and even then I may still stay.
Have you tried calling Geico and asking if there are any discounts? Big insurance companies often offer discounts for all sorts of things- Federal employees, college alumni, professional organizations. Maybe one of them will apply to you.
Also, what are your coverages? You may be able to tweak those a bit to reduce your rates.
EDIT: And Progressive and Geico aren't necessarily the cheapest options. I'd call lots of companies: USAA (if you're eligible) State Farm, Allstate, Farmers, Erie, and I'm sure you have some local insurance companies as well. You might catch one of them at a good rate level and get a deal. I would STRONGLY recommend that you stay away from the budget insurance companies like Elephant, The General, Safeco, Etc. There is a reason they are cheap.