I'd suggest something like the ASUS X200- it's got an atom, but with those specs, I'd say anything will work. It's 11" so it won't take up too much space, and the battery lasts forever. We got one for $200 in an emergency and it's surprisingly capable. Screen is terrible but the keys aren't too bad, and there's space in between them so it might even work with gloves on. You could get the equivalent from dell (Inspiron 11), from their outlet site, for $120. Refurbished means NOW it's reliable, right?
That Chuwi Lapbook recently reviewed on Anandtech would work too- larger screen, worse battery for $270.
Maybe a used Surface 3? It's got a full-sized USB port, and a stylus would let you use it with gloves or dirty hands in the garage? And it'd be easy to hold in one hand? Those seem to run in the 200-300 range used.
But really, if you can get your hands on any old laptop, it'll meet those specs. You need to make the software will run on newer
versions of Windows- that might be more of a sticking point than meeting those wimpy hardware requirements.