Re: Help with large(ish) Wood/foam CNC :)
15mm profile rails (such as Hiwin) would be enough, you won't exceed the rated loads with what you are planning. 20mm rails may be easier due to bigger mounting bolts. They are also taller which may be good if you want a ballscrew alongside, but it's best to minimise overhang etc where possible.
I've had good experience with BST automation on Aliexpress. You want medium (not light or zero) preload ideally and consider getting high precision (rather than standard) which is available if you ask for it.
Most sellers will customise orders and lengths to exactly what you need, so don't be constrained by why they have listed.
For ballscrews you want high lead (10mm per turn or greater). If you are doing mostly wood and particularly foam, I'd suggest 15-20mm lead ballscrews. I recently got some SFE1616 screws from BST and the quality appears quite good (better finish than the classic RM1605 Chinese ballscrews) though I haven't got my machine moving yet.
7xCNC.com - CNC info for the minilathe (7x10, 7x12, 7x14, 7x16)