More than one way to do it, but I think that your original proposed zig-zag is just making more cutting and fitting work for yourself.
pssst, btw, a 1x2 is not "square".
OK, let's see, you have 2x2 posts and 1x2 rails, with the rails 'flat' so the 2" dimension is horizontal. You're welding it all up and grinding the welds flat, and you don't want the tubing to be left 'open' (close or cap the ends).
Like I said originally, although your proposed zig-zag cut would work, I think it will be more cutting and fitting work for yourself.
Three choices I'd go with would be:
- make 'inset' caps that go in the 1x2. Plain straight cuts on the 1x2 and 2x2 pieces. Weld caps into the ends of the 1x2, grind flush and flat. Lay 1x2 on top of the 2x2, weld, grind welds flat (only not easily ground weld would be the inside fillet weld at the inside corner of the 1x2 onto the 2x2).
Pluses : Plain straight cuts on the hollow tubes. Straight welds joining the tubes.
Minuses : Possible fussy fitting of the inset caps into the 1x2 tubes.
Alternate : Put the caps on the 2x2 posts, weld and grind flat/flush.
- Miter the corners, not doing the zig-zag. The angle won't be a 45, but a 30/60 (depending on which face/leg you measure/reference off of).
Pluses : One cut on the tube end, jsut it's an angled cut.
Minuses : Angled cuts (some folks freak out with angled cuts). Having to weld an outside miter-cut corner (if the fitting is off, you have a gap to try and weld on an outside corner).
- Make a 'cope' cut on the 2x2, leaving just the outside vertical 'skin'. Square cut on the 1x2, lay it on top of the 2x2 and butting up against the remaining 'skin' of the 2x2. Weld and then grind flat/flush.
Pluses : Straight cuts.
Minuses : Just have to take a little more time and effort to make the cope cut.
I'd probably go with Option #3.