There's no such thing as a visa that "restarts" again.
A visa grants you a certain number of days when you enter Thailand, and that is your permission to stay.
A multiple-entry visa grants you those number of days every time you enter while the visa is valid.
As there are no 3 month multiple-entry visas, you are talking about a single entry visa.
That means when you enter Thailand, your visa would be used, gone, done, no longer valid. You would just have a permission to stay stamp in your passport. When you leave, that stamp will be cancelled unless you purchase a re-entry permit. If you return with a re-entry permit, you receive the same entry stamp that you left with, and it does not add any extra time. So if you left for 3 weeks and returned, you would only get a stamp for 1-2 weeks in your passport.
It's your money. You can do whatever you want with it. Just know that it will effect your next extension if you fail to meet immigration's requirements.
A Non-O visa is valid for 90 days. But that doesn't have anything to do with your extension. When you enter Thailand you will be stamped in for 90 days. That is what you need to extend.
You don't say what kind of non-O visa you applied for. But the only option for applying a non-O visa is the 1-year extension based on the same reason the non-O was issued. It can be applied for when you have 30 days or less left on your entry stamp. Some offices allow 45 days early.
If you are married to a Thai or have a half Thai child, you may also qualify for a 60 day "visiting Thai family" extension one time per visa.