At that size you really need to stop by a bike shop and try out frame sizes, even on not-electrics. I'm 68" height and I ride an 18" frame, that is the nominal size of the top bar from seat post to handlebar stem. Most bike shops don't even have any stock that small, you may have to stop by the discount store and look at kid bikes, which fit me but have trashy mechanisms.
I've got short legs (28" inseam) and have trouble touching the ground when the seat is adjusted for my legs slightly bent at the crank bottom (correct position) so I ride with my legs bent more so I don't fall over at stops. Legs bent too much slows me down. You may have long legs and could take a longer seat-crank distance.
I won't bend over in the drop handlebar butt up "road bike" position, there is a family history of popped neck disks. You may be fine with a road bike. I ride a cruiser position if I can get one, but for years I rode a kids mountain bike with modifications to get the handlebars back where i could ride almost upright. Real cruisers are single speed, would require a lot of pushing up the hill in this area. Mountain bike in cruiser position messes up the weight distribution though, I had trouble with front wheels skidding sideways and front of bike falling down, throwing me over the bars on my chin.
As far as weight, look for aluminum frame and accessories. Runs the price up, but oh well. You could pick up a steel frame kid bike at a charity resale shop to check out your fit and handling ability for $50, then know more what you want when you buy something new. I just dropped $2000 on my first adult bike in January, and won't be going back to kid bikes anytime soon- premium SRAM gearset, mechanical disk brakes, and an aluminum frame are so cool. Plus real weight distribution design, maybe it won't throw me with groceries in a basket on the back like the mountain bike did.
After trying a used kid bike, you can look for bikes on the reviews (main page) that have various frame dimensions available, to fit your body. One size fits all is not going to work at 60" height, and you'll have to special order, nobody stocks a quality bike that small.
