My tip for saving money: buy as much as possible 2nd hand. You do not need the latest of latest gen hardware for a NAS/Homelab. This is excluding storage, and ESPECIALLY hard drives. Those you should absolutely buy new.
As for setting it up… My recommendation is to use TrueNAS scale with either RAIDz1 or RAIDz2, giving you either 1 or 2 drives of parity, in case something fails…
As for remote access, you can run a wireguard VPN server in a VM, allowing you to access it from anywhere, as long as you’re connected to said VPN.