Hi Master_Wither, welcome to the forums!
It might be worth flicking through the original designs on the wiki to see how RepRaps have evolved. The original 'Darwin' had a moving X/Y carriage above a lowering Z-bed. That gave way to the Mendel with the X-Z carriage above the Y-axis bed, same with the Prusa i3 (what I've got). Axial movement is a negligible effect on quality of prints, compared to acceleration, temp settings, bed adhesion, filament etc. Seems simplest to follow where others have pioneered in terms of axes movement.
For simplicity, assuming you will be using RAMPS electronics, with NEMA17's and a hotend, then these 3 items were 70% of my total parts expenses. I found it more efficient to just invest in a quality Prusa Alu frame and be sure of the result, than try and DIY a wooden frame or box.
To save the cost of that last 30%, you could build a
Duct Tape RepStrap to then print your own mounting brackets...