I don't see any issues with welding the top as a single frame. There are good reasons to do so.
For legs, I would layup and weld the lower framing and then join the top to the frame. That way I could avoid try to set a "long' leg on end and get everything square with long vertical extensions.
Your system shouldn't be having to deal with a ton of side to side movement, mostly up/down weight distribution so 3 beads should give you ample strength.
Others will give opinions as well.
Cheers!
Paul