Extrusions are very accurate, either profile Ali or RHS Ali section. Bit more expensive than steel, but alot of steel is ERW (electric resistance welded) with a seam down one side. I remember reading a post where they wished they'd skimmed the steel section before mounting the rails. Factor in the cost of getting two faces ground and the Ali profile is your best bet.

By the way, in your sketch showing the box section assembly wrapped around the gantry this could probably do with a slight re-arrangement. As drawn the top and bottom plates fit on top of the sides. This means that the sides have to be very accurately cut to get a nice just-right preload on the bearings.
If you make the sides longer, and have the top and bottom plates inset, then the play in the bolt mounting holes (~1mm in total up and down) which are now in the sides and not the top will allow you to put it together better, and set the system up with just the right load. Otherwise you risk either squashing the bearings or pulling them apart.