what kind of frame to get for an oil painting on canvas stretcher?

I have 6 to 12 months before I can varnish and frame my oil painting.  But I thought now might be a good time to start looking for frames at thrift stores or price out how much it would cost to get the frame.

It's painted on this canvas which is 12x12" and for some reason, 0.62" deep (why it's not a fraction, I have no idea and even less idea how to make it into a fraction).  

I tried searching online shops like amazon.ca and Opus.ca (our local framing and fine art supply supplier) but there are too many kinds of frames.  Most of them have glass and a matt which I'm pretty sure I don't want.  The ones at the thrift shops have even less information.  

Where do I even start learning about frames so I can learn about what kind of frame I want to look for?

oh wow.  I am learning a lot.

New, mid-range frames don't come with wire, thingies to attach wire to frame, or the thingies to attach picture to frame (spiky triangles? or are nails used these days?).  These are all extra!?!

With a canvas, you can use just about any frame. The shallow ones can still be used but the canvas will project a bit out the back so it doesn't sit flush against a wall. Some people don't like this.
Deep frame mouldings avoid this issue.

How you attach the canvas to the frame is dependent on the relationship between the frame depth and style and the canvas and how easily you want to be able to remove the canvas at a later date. Nails, staples, framing points, framing points and staples, canvas clips and corner holders can all be used.

You are correct that you do not want matboard or glass for a canvas.

Canvas can also have their sides painted or wrapped and they are hung plain. This is often done with a deep edge stretcher and is referred to as "gallery" style.

There are also " floater" frames, which are only for canvases. They are basically L shaped wood pieces that make a decorative box which is typically slightly larger than the canvas an it sits inside, "floating" in them.

I am also a picture framer, and can say that canvas does not need to be framed with a mat or glass, but glass can be advisable if its going to hand in a dirty area, dusty zone or a  kitchen.
I dont want to take you down the path of teaching you frame design, but a good framer with samples will be helpful.
I always design so the frame blends and does not jump out from the wall.
Some just want anything to protect the edge and some just hand the wire on the canvas stretcher frame.

The teacher in painting class recommended something called inset frame (i think) where the picture is in front and surrounded by the frame on the side.  I'm not sure if I understood what he said.

Putting here to remind myself to look it up.

That is the floater frame. "Floater frame" should be the more search engine friendly term for that style.