By cheapest, assuming you mean the Roku Express. Roku just released a new Express (model 3960) that is dual band (2.4ghz band and 5ghz). Sells for about $30.
You will likely come across the previous models of the Roku Express that are 2.4ghz-only for much cheaper/sale prices since they have been replaced with this newer model. Would probably forgo these previous models and at least consider the Express 3960 as the starting device.
My Ultra 4660 definitely has a better antenna (as least in regards to "reported strength indicator"), but have not had issues with my older Premiere+ 3921 or other devices regardless of their location. Further away from the router, less strength, but still able to connect and stream without issues.
Worse comes to worse, you can always place a wifi extender, repeater, an access point, or even a mini-router in the basement to help get the signal get to their devices.
Personally, if budget allows, I think my default starting device would be the Express 4k+ (3941) because of the better hardware and the option to use ethernet with an additional ethernet adapter purchase if the wireless ever fails and ethernet is practical. However, I don't see anything wrong with the new Express 3960 models if only needing a basic streaming device.
You can see the various models available to you on the Roku website. https://www.roku.com/products/players. I have always purchased my devices from a physical store (Walmart, Best Buy, Target, etc), since easier to return if an issue arises. I have yet to run into an issue requiring a return though.
Roku Community Streaming Expert Just another Roku user... I am not a Roku employee. Insignia RokuTV, Ultra 4660, Premiere+ 3921, Express 4k+ 3941, Streambar 9102