Maybe trying with some Raspberry Pis for your services (takes up less space, low power) and building a dedicated machine for the NAS, as suggested by @hodgepodgin@lemmy.zip, but that’s a whole different budget.

Otherwise, maybe going for some mini-pcs, more recent second-hand PCs (stronger CPU for video encoding) or just more RAM and more disks.

I guess the final price will depend on what exact machine you can get your hands on.