You could go sub 1mm wall thickness, but 1mm should be thick enough to not have to worry too much about strength while machining.

What do you mean by round over? Just a radius on the end?
On a CNC the difference between square, chamfered, and rounded, is a line or two of code. The only problem would be if you wanted both ends radiused internally and externally, as you're then potentially into a second op.