Hey @rnd256
A NAS is a great way to get tons of storage to enjoy offline and in private. The NAS devices are sometimes sold unpopulated (you need to fill them with hard disks) and sometimes sold populated so you can plug and play. The built-in management software allows you to manage the device using a web browser, similar to your home router. You will need to set up at least a user and password and shares to get it working as a network file server. The better models can also run apps such as filesharing clients, seeing that they are online 24x7.
Some words of warning though. NAS devices put out heat like a PC does, so ensure it is placed in a well-ventilated area. NAS devices also have spinning hard disks and fans which can result in varying noise levels, so be mindful where you place it. I know that a lot of people do not have theirs in a bedroom or near the TV.
Connectivity suggestions.
Option 1:
Could you not run the single cable from the NAS to your router? The cable can be up to 100m long and you can buy various ready-made lengths of Cat6 Network cable online. If you are renting you can likely not make holes to run it in the walls, but thin PVC trunking can be stuck down to tidy things up a bit, or hot glue the cable itself.
Option 2:
Try "Gigabit Powerline Network Adapters". They are sold in sets. You would plug one into a power socket at the router (as well as a short network cable to connect the router) and another at the NAS, plus a short network cable to the NAS. They would then use your house's power cables to send data. Just like WIFI, these can also be prone to some interference. Your mileage may vary.
Option 3:
Try a "Wireless Bridge" which looks like a WIFI access point, preferably the same brand as the WIFI router downstairs as it may reduce setup problems. It would be placed next to the NAS with a short network cable to the NAS. Many general WIFI access points can perform this function when set up in "bridge mode" where they are set to be a WIFI "client". I would only consider this if your WIFI signal and throughput are very high where this is to be installed and you have no other option.
Hard disks such as the IronWolf range are more expensive but more durable (they will be powered on 24x7 after all) and have a longer life expectancy.
Just a note that most populated products are sold with RAW capacity. Once you initialize the disks, you select a RAID level (5 is budget-friendly and what you are looking for) and the disks are formatted and you effectively lose one drive's capacity for redundancy. This means that a 4x12TB RAID-5 will give you a usable 36TB space.
Now for a final word of warning. You will find much advice out there on the topic "RAID is not a backup". It protects your data from a single drive failure. You have to replace and rebuild the failed drive urgently when this happens, but in the meantime, you can still access all your data.
If a second drive fails before the first failed drive is replaced, you lose all data.
If files are accidentally deleted, overwritten, corrupted or damaged by ransomware, the damage is instant across all drives, so your data is generally gone. Some snapshot features can mitigate this.
If the NAS is stolen, dropped, struck by lightning, or your house burns down, your data is gone.
If you are happy to redownload your whole video collection if tragedy strikes then you are set. However, if you have any data that is irreplaceable such as personal photos, then make sure you also take offline and offsite backups of that data regularly.
Have fun.