Above you see the basic sorts of canvas. The lower one is linen. This particular linen is Claessens type 12. Its a very fine oil primed canvas made in Belgium. Linen is made from flax and is usually brown in color. The oil primed has a distinctive sort of silky feel under the brush. Linen is better in every way I can think of than cotton, except it is much more expensive and comes and goes a lot as I have described in a earlier post . Good linen is oil primed, as long as you are going to pay for linen get oil primed not acrylic. I should pause and mention that I assume you are painting in oil, you can not paint on an oil primed canvas if you are using acrylics, but you can paint on an acrylic ground in oil. Fredrix makes several nice oil primed linens, I have used the Carleton and the Kent. Kent doubleprimed is a great canvas. A 54' by 6 yard roll will cost nearly 400 dollars. When it arrives you pry the metal cap off the tube and it smells so good, its a mixture of linseed oil and the flax, not as good as an old fashioned restorers shop doing wax relining and varnishing but close. There are advantages to both linen and cotton and I am myself conflicted on this so you should try both and make up your own mind.
The upper canvas is a primed cotton. Both of these canvasses have been sitting in a corner of my studio for a year or more. The linen is loose on its stretchers and if there was a painting on it, in a gallery that would be a problem. The cotton is of course as taut as the day I stretched it.
If you wanted to beat this problem one way to do it of course would be to mount your linen on a panel with glue. There are companies out there that sell mounted canvas on hardboard but I find them expensive and am capable of mounting my own in any event. I would spend a lot of money on panels if I didn't make my own. Incidentally I should mention that all of this is leading up to a tutorial on making top quality panels at home. I probably paint 70 or 80 pictures a year, but I only show about half of them. Many of those that are not shown are rough sketches or are not my best work and end up destroyed. Mounting canvas works best for smaller pieces. Over about 18x24, weight gets to be a problem. I usually paint on a primed panel below that size anyway. I like painting on panel a lot and I have a way of oil priming them quickly and easily.
If you look at the stretched canvasses above, you will notice I have left a fair amount of extra canvas turned over on the back of the stretchers, I do this for several reasons. If I need to tighten the canvas up later there is something for me to grab with my canvas pliers, and if I really have to, I can add an inch to one side of my canvas to save a painting with a design fault. This takes a bit of finessing, I guess I will have to address that trick later but there's a lot of other things to explain first. One of the things that make most hobby shop prestretched canvasses so despicable is that they leave you no selvage turned over on the back and if you want to tighten up the canvas they expect you to key it out. Keys are a bad idea I will explain later. Also it is common practice to wet the back of a canvas to make it taut again. Don't ever do it again. At least not often. I will tell you why later.