But back to toilet problems. I just looked at it and it was leaking out of the handle. The tank was almost filled to the top. I have no idea why. When the toilet initially fills after a flush, it fills to the fill line. Apparently, the tank has been filling on it's own for some reason.
Of course, as you know, that water shouldn't be anywhere near high enough to cover the handle inside. Mine is about 2-3 inches below the handle and would hit the overflow pipe far before reaching the handle, which would cause it to loop and keep trying to fill up as it drains. Sounds like something is wrong with your fill valve and possibly the overflow pipe is too long. Did you just move there or something?
Pick a day when you have a good bit of time and drop by a Home Depot, Lowes, etc. For about $15 to $20 max, you can get a full kit with every kind of washer, bolt, etc, that you would need.. It has the fill valve, flapper, overflow pipe, new bolts/washers for where the tank joins the toilet, etc. Everything that you would need. Its like a tuneup for your toilet. Very easy to install, just can be time consuming.
You may as well check where the tank joins the bowl. Use a cell phone or cam to take pics of the bolts. I'll bet they are rusty. There are only two bolts that go through the ceramic and tighten down to hold the tank on. There is only a simple seal that keeps all of the tank water from pouring out of the tank. A lot of people sit down and lean back pressing on the tank, but aren't aware that over time the bolts rust. When I changed outs a while back, one of the bolts had virtually rusted through. Those have to be changed after typically a high x number of years, particularly if the tank sweats from cold water that runs down onto the bolts constantly. You may not have any issues with that now, but if you're going to change one thing (sounds like the fill valve is having issues and I'd just replace it considering how cheap it is), you may as well change it all and not have to worry about anything else.
I took my whole tank off a few years ago, washed out all of the crud out, dried it, changed all of the washers, valve, flapper, etc. If I can do it, anyone else can.