I've never though about that! But it sounds great! A question though... I don't know how much though you actually have put into this, but I'm curious. What do you consider a cheap computer?
I do all my coding (though it mainly web, which arguably might need less resources than other languages) in a medium tier pc. It's a lenovo B590 with an i3, 8GB RAM. It's not exceedingly fast but with two windows of chrome, 20 tabs each, 5 or 6 instances of PHPStorm open, and all the usual programs (email clients, dropbox, chats, etc) it still feels quite snappy.
The cost here in Austria was around 650€ or so in total, maybe less (I'm not quite sure now because I upgraded it little by little).
My question is if your plans are set around a dirt cheap machine that you "wouldn't care at all" if it gets stolen, lost or broken... Or something more in the lower middle class where you'd have to be careful not to lose one per month, but you could still run most of the stuff you'd actually need for local development.
This question arises mainly for my concern is greater about not having a working reasonable internet connectivity hence making it difficult to work over ssh, rather than the laptop getting stolen or broken.