You must have a raised edge on the outer lip of the stretcher or their will be lines where the wood touches the canvas. Quarter rounds are not a bad approach to getting this edge, but I would lightly sand the quarter rounds so that you don't have too sharp of an edge. This would be particularly important if you are stretching a canvas giclee print but also for any canvas substrate.
As a framer, I cannot tell you how many canvases come in with the canvas stretched on the wrong side of the stretchers.
Eventually these canvases will have lines visible on the paintings.
You might also consider putting a barrier layer of polyurethane varnish wherever the canvas contacts the wood to prevent migration of lignins or other damaging substances from the wood to the canvas.
The center supports will help prevent warping but will not eliminate the problem. They are primarily intended to keep the stretchers from bowing during the stretching process. Only two approaches to eliminate warping: #1 ~ use a heavy enough stretcher #2 ~ Frame the piece with a heavy enough moulding to prevent the problem.
After stretching it is a good idea to attach a polyflute or foam core board to the back of the stretcher for two reasons. It will help to eliminate any physical damage to the painting during handling from the back side. It also will keep dirt, bugs, etc. from getting behind the canvas. This is common practice when custom framing canvas by quality frame shops. If you are not framing the piece (gallery wrap) this should be another step taken to protect the art.
If hanging the canvas without framing I would suggest either using WallBuddies http://www.wallbuddies.com/
up to about 60 lbs. or BeeHive Hangers up to 30 lbs. http://www.beehivehangers.com/
. They will hold the canvas flush against the wall and level. I would consider using Z-Bars if heavier http://www.zbarhanger.com/
Strainer stock is available in 10' length from framing distributors in various weights. This is lumber milled with the raised lip. Also, custom stretchers are available on line which will allow for tensioning the corners.
Prior to stretching any canvas on stretchers be sure to measure corner to corner on the diagonal
in both directions to make sure the stretcher frame is square. Otherwise it will be difficult and costly to frame in the future.