Salty, on the motor side of things the cost of properly setting up a lightweight system is going to be pretty high. You'll likely want lithium to complement the need of having an easily lifted folding bike, which starts at around $400CAD. The best motors to pick from in that category are the Nano/Brompton Nano, the BionX 250/PL250/PL350's would suit the application well, my particular preference for a folding bicycle would probably simply be the PL250. These aren't powerful motors at all in contrast to what others will put out, but they'll be more than enough to help level out your physical output and keep you from becoming overworked.
There are other lightweight options to choose from such as those that use the bicycle's own drivetrain (Cyclone, Currie, eLation), these allow you to utilize the gearing on your bicycle too, which works out to good efficiency and performance - but these kits *do not* have the same sort of hardiness against the elements that a motor such as BionX will, and I would not personally suggest them for use in winter. Another reason that I would suggest a hub motor over a frame motor in this case, is that if you're working with a tight weight budget as you might be on a folder, the hub motor supports its own weight whereas the frame motor sits upon the bicycle and acts to put force downwards on the tubing itself.
I don't have any personal experience with the Nano system, but i've nothing but praise for the BionX. These kits are very well made, very user friendly, and they're designed in a way that encourages exercise as opposed to using your e-bike like a lazy old scooter.
I do have some input though: a half mile isn't a terribly large amount of distance to pull on a normal bike, let alone an e-bike, and batteries don't care if you've gone 2 miles or 40. 600 charges is 600 charges, and batteries lose charge on their own, they don't wait for you to go 2 miles 20 times.
I don't personally feel that the situation really warrants the e-bike, but ultimately its your decision and i'll just provide input
. You may also find that you'll be limited by some of these folders when it comes to doing errands, if you're already close to the carrying capacity. I would try and find one that has a good weight rating on it so that you can have a rack and some bags too if you want them. Potentially, you could run something like a Mu SL + PL250 and have a system weighing in at about 33lbs, but the weight limit on the system would be quite low.