The only 2 'cheap' NAS I'd consider would be something like the ASUStor Drivestor2 AS1102T or the Qnap TS-233, not really a big fan of the Synology stuff.
Just about everything else NAS will be well above your budget although most have Quad Bay or more if you choose to use a Raid10 etc. All the single/double Bay designs will be restricted to standard or Raid1/Raid0.
A Good NAS isn't cheap, for a pre-built design, but it's entirely possible to take an old Dell Optiplex or similar mini-tower and Build a NAS yourself, using a Linux based OS, at which the biggest expense will be the drives. The pre-builts do have advantages over the home built NAS, such as most use a hot-swappable drive system and multiple high speed ethernet ports that your standard mini-tower pc isn't equipped with.