If you want it just for Time Machine - the Synology DS223j. Soon after you get it you'll see all the uses and which you purchased a better one.

Get an entry level Synology single or double bay NAS + a 3.5" Western Digital Red Plus drive of sufficient size. I wouldn't rely on a router. A router's primary purpose is to connect your devices to the Internet. Storage is an afterthought. Let the router do router things. Get a storage device (NAS) to do storage things.

This brand has a long-standing of reliability and trustworthiness in this category. They have excellent long-term support. Feature updates (e.g. the newest DSM WebOS) are often even pushed out for 10-year-old hardware - you'll find it hard to find that level of support elsewhere. This NAS has 2-bays, storage up to 2x108 TB (theoretically speaking), companion apps, and its UI runs in a WebOS-System within the browser (and is therefore not bound to any operating system).This brand has a long-standing of reliability and trustworthiness in this category. They have excellent long-term support. Feature updates (e.g. the newest DSM WebOS) are often even pushed out for 10-year-old hardware - you'll find it hard to find that level of support elsewhere. This NAS has 2-bays, storage up to 2x108 TB (theoretically speaking), companion apps, and its UI runs in a WebOS-System within the browser (and is therefore not bound to any operating system).Single-button press backup functionality (ports and button on the front): This function is called USBCopy. You just need to attach your media to the front, press the Copy button (labeled C on this version) and wait untill it's done (no need to have it attached to any PC and no need to login to the NAS as well). By default, the backups get compressed to a single archive per backup and are named after their device name and timestamp attached (changeable within the settings). Older/other versions also had an SD-Card reader, this one doesn't (but it seems to have an eSATA port) so you might search for an alternative if you need the SD-Card reader. | DiskStation Manager OS is rock solid: DiskStation Manager OS is by far the best commercial NAS-OS out there when it comes to expandability, usability, and stability. No other system comes close, unless you build one yourself and use an Open-Source NAS-OS that you fine-tune to your needs. | Synology has by far the best LTS of any comparable manufacturer: Even 10-year-old NAS storages still get updates for their OS (called DSM). The only thing that limits you is the hardware. | Full flegged x86 CPU: See this for tech-spec. | AES-NI hardware encryption engine: Encryption performance at over 113.01 MB/s reading, 111.66 MB/s writing. | Too many variants, pricing is not always logical: With, without an SD-Card reader; with, without a copy button and front ports. Model numbers also don't seem to follow any logic so you have to be careful when buying here. Also with some, you can switch the RAM model yourself while on many others it's soldered to the mainboard. You don't need the latest model. Be careful selecting one to fit your needs and pocket when buying (they're pretty good even when they're used - just use new HDDs and you're fine). | Not made for 4K streaming addicts (PLEX): Yet so are typical other NAS from other manufacturers unless they are tailored for the purpose. Synology calls these NAS boxes "play" e. g. DS216play. They often have other drawbacks. · You have to spend more to get hardware level support for proper media-streaming. This is, however, not the usual task for a NAS and is only interesting if you need to stream 4K files (most often other bottlenecks are in-place like a slow network connection anyway). For streaming 1080p this NAS should be fine. · If you need serious streaming look elsewhere. | Requires a bit of work if you want to get the most out of it: It's clearly not made for people that want to buy a device and just use it but those that take some time to set it up. Once you're done, it runs, and runs, and runs (till you want to do more, which you can since it has Package-Management built in that enables you to download new packages and extend the functionality of your simple NAS). | Company-level advanced BTRFS file system with built-in data integrity check: See further details on Synology's page | Usability (WebOS): Product and software work seamlessly with any operating system (since it's a WebOS running in the browser). Product software has easy to follow icons and GUI that allow users to use it as a VPN, time machine, media server, etc. | Expensive: While the cost is not as high as some, there are similar storage size options for cheaper prices. This price tag, like most, is for branding and the high quality product you get from Synology. | Slow support: Technical support is not the go to option for a solution, with long wait times, and open cases taking up to weeks to resolve (that is with persistent follow up). | Options: Do you need 2 bays, 4 bays? Diskless, or up to 32TB? While prices will vary between size options, there are enough combinations to choose from for your storage needs.