Hello Klossie
Such a difficult question to answer as it depends on so many factors. Your best bet (and I appreciate it's nigh on impossible at the moment), is to try as many different bikes as you can, and as many different drive train options as possible.
How tall are you and how much do you weigh? How long and how steep is the hill in question?
There are certainly several e-bike companies on this site, who will have bikes to suit you, that are also in your price bracket.
My Wife has a Wisper 705SE. Whenever we go out, I'm reminded what a good bike it is. Pop the saddle up a bit and it'll haul my 16st, 6'4" frame along quite nicely. My Whyte has an 11.4ah battery and does the job nicely, but I wouldn't want a smaller battery than that (having said that I'm looking at my Wife's Wisper battery and am surprised to see it's a 36v 8ah battery!). You really want to be in double figures for ah - 13 is a good target. Had my Whyte Coniston not turned up unexpectedly, I'd have bought a Wisper 905.
The Woosh Big Bear is a good shout, although Woosh have several other models that might suit your needs.
Happy bike hunting!
Gaz