(Solved)
This will be used in CLI mode to do some tiny programming and text file note-taking. Having WiFi would be nice. The price has got to be CHEAP. ARM is ok.
OP decided to kill windows on the Timberborn machine and go with Debian.
The hard part is tiny: 10" diagonal screen and really cheap: like milk money cheap - - Perhaps a netbook would work, some of them were Linux based right?
I got a $12 10 inch Asus eeepc 1005ha that I have NetBSD with i3 on and it's perfectly usable, so something similar to that would probably be fine for linux cli stuff as long as a 32 bit cpu is okay
$89. The alternatives are $180+, so this is about as good as you're going to get unless you go second hand, and most of the time second hand is more expensive than new because people want to recoup the costs as much as possible without actually thinking about what a fair price is.
Netbooks, haven’t seen them in a decade. They were sluggish at best even running linux. The screens were awful. Seriously, I can’t recommend. A refurbished 10” tablet with a bluetooth keyboard would work 10 times better.
You don't really need one that is specifically Linux based, as you can format a windows box to Linux at will. Really any 10" laptop you find on cragslist or ebay should do.
Honestly, the only difficult requirement will be the 10" part. 12"-13" are much more common for small laptops.
The Asus EeePC 1000H that I bought back in 2009 is a 10 inch monitor netbook. 160 GB HDD because I didn't go with SSD, only came with 1 GB of RAM and cruicially was offered in both Windows XP and Linux flavor which was a bit niche at the time.
Its 32-bit single core (hyperthreading) atom processor is very slow at 1.6GHz, but it can still be used with antiX for my usecase.
If you manage to get hold of one of these old dinosaurs, I'd probably opt for an SSD solution, that's a pretty big bottleneck.