I would say Arch if you are that tight on resources and comfortable doing so (the setup isn’t as bad as people make it sound, just look up a guide online), but Endeavour would get you to more or less the same place with much less complexity.
That said, is there any chance of upgrading the RAM? an extra 4GB or 8GB stick of DDR3/DDR3L off ebay would not cost too much, and would make a world of difference for things like modern web browsers.




Depending on your budget, I often find there are good refurbished deals on semi-recent models on ebay. That’s how I got my current laptop. Most business models will have upgradeable RAM/storage/wireless cards. Externally removable batteries have not been a thing on laptops in a long time, but replacement batteries for common business models should be available as long as you are okay with taking off the back lid, which it sounds like you are.
A quick look on ebay (Your local market may vary) suggests there are some decent deals on 11th-13th gen 13" HP/Dell/Lenovo business laptops in the $300-400 range. Maybe something like this HP 630 G10?
If your budget is less, the usual 8th-10th gen Intel business laptops are always a good option and usually go for $100-200, maybe even under $100 once you get into some of the lower spec or scratch-and-dent models (Also, yes, I know AMD is a thing, but businesses almost always use Intel in my experience). My travel laptop is an old 8th gen Acer Swift with a dent in the back lid, but it otherwise works fine and has handled many trips in my backpack. Maybe something like this Dell 5310 with a scuffed lid? I’m sure you can look around and find something which works for you.