Interesting design, it is ambitious for a first build!

If the aluminium pieces you need to machine are small then a mill style is a better option. But if the pieces are fairly large then a router is required but be aware it will not be as stiff as the mill. To maximise the stiffness of the route I would avoid cutting long slots in the bed and gantry frames as this will reduce the stiffness noticeably (from a box to a U channel), and even adding the L bracket will not recover much of it. I wouldn't make that choice just to protect the ballscrews. Go for stiffness in the basic structure first, then add external ballscrews, and then add brush covers over the screws if required.

15mm rails are a bit small on X and Y, go for 20mm instead. On the Z then 20mm is also fine with 4 rails and 8 carriages. If you drop to 4 rails and 4 carriages (I'm guessing you mean mounted around the lowest part of the Y axis box) it will still function but you will have lost a fair bit of the advantage of the box Z structure. I would say either go all out for 4 rails / 8 carriages, or go for simpler conventional Y and Z, not something in between.