Hi, StelioKantos_US.
For NAS build the current sweet spots appear to be either the NAS Killer 4.1/4.2 or the SNAFU, depending on what hardware you find available when you go looking. It sounds to me like the NK4.1 is the better deal if you can find the hardware readily. Either one is going to provide plenty of horsepower for NAS + any of the *arr dockers.
Run a QSV transcoder on any inexpensive Intel box with a 6th generation or newer quicksync capable CPU. The current value deal for this is the HP Prodesk 400 G4, around $90. Do your 4k streaming only when direct, and this should meet your needs nicely. Transcoding 4k is not recommended.
Without new disks this should be doable for around a quarter of that budget, so spend what you like on storage after that.
Links:
NK 4.1: [Guide] NAS Killer 4.1 supplemental + deals
SNAFU: [Guide] Anniversary 2.0 "SNAFU" - Server Needs a Friggin' Upgrade
QSV Guide: [Guide] Hardware Transcoding: The JDM way! QuickSync and NVENC
HP G4 Owners Thread with links to the current seller: [Official] HP Prodesk 400 G4 SFF Owner's Thread
Hope this helps!