An awful lot of the Intel low power and cheap stuff after Bay Trail-T have been quite good for their price. Cheap but you don't really get much of a laptop in the sub 300 dollar range anyway, you can almost always disable secure boot so if you want Linux it might be possible. Very energy efficient but really designed to blur the line between phones + tablets to laptops so it sacrifices a fair but to make that possible, a lot of 2 in 1 hybrids like Asus Transformers and Acer Switch series use the Intel Atom processors which arn't bad just not great.

Models with decent battery life and performance are priced in and around 300 euro / dollars, don't make the mistake of buying the lower price sub 10 inch models like I did. I used to have a Linx7 which for what it was could do almost anything I wanted (I could play HL2 between 25 to 40fps bu it oddly struggled with the first Deus Ex) but and poor thermal characteristics meant when I put it under a bit of stress its battery tanked so it just couldn't really be a daily driver but it was great at playing back media and did a great job browsing the internet just that battery was crap, its screen was also a little two small to do anything but in landscape mode with a stand and a bluetooth keyboard I managed to get a couple project reports written for college without any problems (windows 8 and 10 on screen keyboards are quite good for a device that size).

It all comes down to how cheap you want to go. I'm in the market myself for a new small form factor cheap passively cooled laptop / hybrid myself and I've been eyeballing something like a Asus Transformer Book T100HA (4gb of ram, 64gb eMMC storage, Atom X5 8500), now I know for a fact you can manage Win8.1 or 10 reasonably well on as low as 1gb of ram so 2gb isn't that bad when you temper your expectations but no matter what you get make sure it has more than 32gb of storage space because that shit was barely usable. Acer, HP, and I think Toshiba have 2 in 1 convertibles that include a slim HDD in the keyboard dock.

All that said you can program on almost anything, its all a question of how cheap you really want to go.

One popular opinion is to buy an old computer off of craigslist or the like and reformat it with linux. Or you could get a single board computer like the raspberry pi if you wanted an arm processor.