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.
Given the tight budget, here is what I would do, especially if you are not too constraint by space and don't mind a few extra watts of power consumption. The Raspberry Pi are getting expensive, and the 200USD will barely get you a RPi5 nowadays. You said there is no market for you for second hand sever hw, but I'm guessing it should not be too hard to get used office desktop PCs.
Get two of these. Maybe Optiplex or Thinkstation. You can probably get something decent <50USD each.
Get two small SATA SSDs for the OS (128 - 256GB), around 30USD each.
Get your storage drives. You should get 3 of them so you can have ZFS raid redundancy.
On one machine, install TrueNAS and your storage drives. Default RAM is probably enough.
On the other one, upgrade the RAM to 8 or 16 GB (~50USD), install your favorite Linux distro, and you can run your services, accessing the storage with NFS!
To me it feels safer (against my own mess-up) to separate the storage and the services, plus this setup is fairly upgradable. You'll probably have space to add more storage drives, even maybe a cache SSD; increase the RAM; add a third machine etc.
Of course it's just one idea, maybe other another layout might fit your use-case better, idk.
Après bien quelques heures sur Megabonk, j'ai pu finir le niveau de la forêt (Tier 3), et j'en suis à 75% des achievements sur Steam. Ça progress gentillement mais j'arrive maintenant sur la catégorie des achievements débile, du type tuer des cactus avec des épines ou tuer des mobs avec une tornade depuis une tornade.
Thanks Mr. Frog! Very cool!