What is an good quality Canon camera under $700?

I have a Nikon now that does not have a removable lens, and it is not a very good quality. The shutter speed is horrible, and I want something that will take quick, good-quality pictures, and in time, I can buy more lenses for.

Then you want a digital single lens reflex camera.

From Canon those are the EOS series, where either the Rebel T3i or T4i would be good starter cameras. The T4i is the latest model. You can pick up T3is with a lens package for less than $700.

That being said - The Nikon D series cameras are just as good, probably better. You can also get a Nikon D5100 with lens package for less than $700.

Either camera is wonderful.

Whether you buy a Nikon or Canon dSLR, how your images turn out has to do with your skills using the camera, NOT the camera you use.

That said, the Canon T3i/600D and Nikon D3200 are both good entry level cameras and during the Christmas season, they are on sale for under your budget

Visit a proper camera shop and hold both in your hands to see which one feels best to you.

Picking a camera based upon your experience with a P&S is not necessarily a good indication of what the dSLR performance will be.

Buying a DSLR on a tight budget is problematic, because nobody really tells you just how much other gear you will need/want on top of the camera.

Even if/when you DO find a DSLR plus lens in your price range, there will always be way more expenses ahead.

You'll want and/or need a few other things such as tripod, filters, a bag, sensor cleaning gear, a second battery, memory cards, perhaps a remote shutter release etc.

That's just the small stuff - I can guarantee you that you'll also want more lenses. You'll probably buy cheap ones at first, then regret that, then start saving for the good quality ones, instead.
You'll also want a decent flash some day.

See how that list just goes on and on?
Owning a DSLR isn't cheap - at least not until you have built up a nice stash of gear. When you look at an advertised kit price, you do NOT see all the other gear that you'll need/want with it.

Just some food for thought… I'm not trying to talk you out of this, just trying to be helpful in case you haven't thought about all this yet.

Please understand this, too: even the world's BEST camera will take lousy photos in the wrong hands.
You need to LEARN how to create good images, they won't simply happen just because you bought a decent camera.