I have used both round and square material for four links, either will work fine.
Just throwing another idea at you here, IMO maybe consider using rectangular tubing on the lower links if you have room. You can always taper the ends for clearance and a clean look. .120 wall min. Depending on weight, possibly even plate the sides. Same for the top links, but no need to plate them.
I recommend using a poly bushing of some sort on the axle end and if you don't mind spending a few extra bucks, get some Currie Johnny Joints for the frame end, they are greasable and re-buildable (you would probably never have to rebuild one on a street application). You can get them where you just weld the sleeve to your link or you can get them with a threaded end like a hiem. I agree with ratty 46, hiems transfer a lot of vibration and have zero give, bushings and Johnny Joints are a little easier on things, not to mention quieter.
If your budget minded just use bushings on both ends, just keep in mind you won't have any adjustability once everything is welded up. If you use a hiem or Johnny Joint you can make pinion adjustments if needed.