I would also consider a low end Gigabyte Brix system. The specs depend on how it's being used. A low profile mATX HTPC (desktop) case with mATX motherboard remains a good low cost option.
1. An HTPC is essentially a low power, low cost PC. It's hardware and software are typically configured to watch video on a big screen TV and listen to music and movie sound on an A/V surround system. (Depending on the user's requirements, it can be configured to do less or more but then starts to deviate from a pure HTPC.) The form factor, software and the addition of a wireless (RF or IR) remote, compact RF keyboard, RF mouse and optional tuner card are what differentiates an HTPC from an ordinary PC.
1. Easy to use interface usually consisting of dedicated media player software.
2. Low power requirements, low noise, low cost, nice aesthetics (HTPC case.)
1. More flexibility. It will do just about anything a dedicated media player will do without the artificial constraints imposed by media players. It will perform additional tasks like recording TV. That's a big advantage for OTA TV.
2. Upgradeable with new software and hardware. New software will extend the life far beyond dedicated media players.
1. Higher initial cost. However, because it's so versatile it can take the place of several proprietary media boxes, potentially lowering long term cost.
2. Takes more work to set up and configure.
1. NUC, mITX or mATX architecture in a compact, low profile case.
2. Low end CPU with integrated GPU (APU.) This can be a standard desktop APU or an integrated APU such as an Intel Atom or a mobile APU mounted directly onto the motherboard. Mobile chip solutions are especially suited to HTPC use since they are typically very low power and often silent (fanless.)
Once the requirements are determined, the solution becomes clearer. Those include things like the need for recording OTA, desired streaming services, type of content, network configuration, software to be used, additional activities (like gaming,) etc. An HTPC will do almost everything a proprietary media player (like Apple TV) will do and a lot more. It just takes some extra effort.