Another one here who would suggest someone in your position should avoid e bikes. My commute is 17 miles each way from the flat lands west of Manchester, but I am fairly familiar with some of the the roads you will be using.
Cheetham Hill Road isn't bad as a climbing experience. IMHO steep enough to give you a welcome lift on the descent, but not so steep as to make a climb unpleasant. IIRC there are a couple of junctions where the cycle lane takes you around traffic lights, which is good. (Although that may be a false memory as it was after midnight the last couple of times I was riding up the road
) Although slightly longer, you could always try Bury New Road as an alternative and cut across at Higher Broughton and travel up Leicester Road, to see how you found the climb/traffic.
As suggested up thread, on the slopes just sit back, relax and spin your way up.
One area I would definitely check out, would be where you approach and cross the M60. If you are coming down Heywood Old Road to get onto Middleton Road and then past Heaton Park you will need to cross the motorway at junction 19. I thought the junction was priority from the right, i.e. free for all. So I would be looking to see what the traffic is like at the times you intend to travel and how you get across the junction. According to Google maps, there seems to be a footbridge, but I don't know if that has restricted access for bikes and how easy it is for a bike to get on/off it. (Assuming bikes are allowed).
As
@I like Skol says, its handy to have a plan B. If only until your legs get used to the commute.
