Consider the Yamaha XT225, also called the Serow. Was made for several years and up until recently. Just check it has electric start (for sure the later ones did, not sure about the oldest ones). There are lots of these, so shop around for good price and condition.
Also, Kawasaki KLR250, a bit bigger and heavier than the Serow.
Kawasaki Super Sherpa, silly name but a decent bike, 250cc, lower seat height and not bad off-road. Electric start.
An older bike will be more affordable, try a Honda XR250L, made around 1991 but really good off road. Kick start only but usually easy to start. Any Honda XL250 might do, but we are talking much older, like in the '80's.