Like normal bikes, e-bikes either have enclosed low maintenance ‘Hub’ type gears in the back wheel (handy because you can change gears at a standstill) or open derailleur gears. Cheaper bikes have 7 speeds, up to 11 or more expensive models. With the exception of the Yamaha motor, they all have just a single front chainwheel, as the electrical assistance obviates the need for lots of gears.
Both gear types are fine if properly serviced, but either way a decent range of gears with a reasonably low first gear is needed in hilly areas.
So that is at least 8 gears for a Derailleur model, and minimum 8 for a hub geared model.
As regards Derailleur gears, 8 and 9 speed geared bikes really need an 11-34 tooth range cassette (rear gear cluster) as a minimum for hilly Sheffield use, and an 11-36 tooth cassette will make life noticeably easier. 10 and 11 speed models can offer a more ideal 11-42 tooth range, or even 11-46 for a really low 1st gear to tackle steep hills in comfort.
Hub gear wise Shimano ‘Nexus’ 8 speed is ok for Sheff, but the 7 speed will be hard work unless paired with a stronger than average motor, as it only offers a 244% gearing range, equivalent to an 11-27 tooth 7-speed (cog) cassette. Thus with a typical chainring and rear hub sprocket combination of 40/19 the bottom gear is a high 36 inches, enough only for moderately hilly terrain, but at least the top gear is a nicely functional 88 inches.
The Nexus 8 speed hub has all the same benefits as the 7 but with an extra gear for a wider 307% range, equivalent to an 11-34 cassette, so a bit better for hillier terrain, although some of the gear steps are a little wider as a result. The same 40/19 ratio gives a bottom gear of 30 inches and a top of 92 inches. With a rear hub sprocket of up to a max of 22 teeth fitted to the hub 1st gear can be made as low as 26 inches, great for steeper hill territory. (thanks to Edinburgh cycles for those details.)
Shimano have recently introduced an e-bike specific 5 speed hub gear, found on such as the cube compact-hybrid , but paired with the more powerful ‘Performance line’ Bosch motor which will have enough oomph to compensate for the narrow gear range. (The wider range derailleur gear version manages with the less powerful ‘Active Plus’ Bosch motor.)
Shimano’s ‘Alfine’ 8 speed hub is the premium option – same gearing as the Nexus but higher quality internals and a more user friendly trigger action. (An Alfine 11 speed hub is – rarely – also available on a few expensive models.)
Innovative systems like the Pinion gearbox fitted to the gudereit-et13-5-evo look like the ultimate transmission option if you can afford it..
A recent innovation is automatic gears – a clever system using the Enviolo stepless hub paired with the bikes command system such that you simply choose and set the number of times a minute you want to push your pedals round (your cadence), typically around 50 – 60 (more is better for battery economy) and the brain and hub will work together you keep that pedal rate steady for you regardless of speed/hills etc, without you having to do any gear changing at all! An examples would be and Riese & Muller swing-automatic
Note: Do try and avoid the e-bike trap of letting the motor do all the work in high ‘lazy’ slow turning gears, even unwittingly. If you can comfortably do so, keeping your legs spinning at a reasonable lick significantly reduces strain on the motor and the draw on the battery, so change to a lower gear promptly, just as you would on an unassisted bike when you are making life easier for your own leg/lung ‘motor’! This maximises the mileage available from each charge and therefore the overall longevity of your expensive battery.!
Bosch say cycling at between 50 and 80 revolutions of the pedals a minute really helps reduce the draw on the battery, so maybe choose a gear that means your legs go round at least 1 revolution every second if you are wanting/needing to max how far a charge can get you.