If you live in an urban area, I would highly recommend a Brompton. It does fine on bumpy roads. Folds up very quick and you can you use as rolling luggage or shopping cart when on transit or in a store. The gearing is quite nice and i can go above 20mph easily on flatish ground.

Also consider looking at touring bikes. You’ll get wider tires, good gearing, and more robust frames. Might get a good second hand value, or some luck with sales if those styles aren’t popular at your LBS.