Toggle redstone circuit

I need a redstone circuit that I can't figure out how to make. You step on a pressure plate: a piston extends, and stays extended until you press a button. This seems like it should be simple, but I can't figure it out. I can't just make it a lever; it has to be a pressure plate to start.

This is how it starts. And that's great. But when I step on the pressure plate:

The redstone dust comes off. So when it retracts again, the circuit is supposed to be off, but now it can't be turned on anymore. Is this possible? I have a limited space to work in (not this testing mountain), but I can expand it if necessary.

EDIT:

So now I have the basic circuit down (from D-Inventor) but I have more problems.

You step on the pressure plate, it pushes in, but when you activate the other side, it doesn't undo unless the button is right on top of the dropper. Something weird is going on here.

(Also: if someone tells me how to upload a zip file I'll give you my minecraft world this is in.)

Solution 1:

It looks like you need a memory circuit. You can face two droppers into eachother. The pressure plate powers the first dropper, the button powers the second. You need 1 item inside one of the droppers. If you take a comparator output from one of the droppers, you can enable it with the pressure plate and disable it with the button.

This is what it looks like. The redstone lamp would represent your output. The signal has only a strength of 1 though, so if you place some wires, make sure that you insert a repeater first.

If you think droppers and comparators are too expensive, you can also make one with just torches and a repeater:

Once again, the redstone lamps represent the outputs. You'll notice that the two lamps are opposite of eachother.