Welcome to SRP!
King Cutters are fantastic razors - I have two of them so far - so it would be well worth the effort to have that one restored. However, due to its sentimental value, make sure that if you do opt for restoration you send it to a pro. You don't want just anybody messing around with Grandpa's razor! And if you choose to do it yourself, don't go anywhere near that gold wash with metal polish or anything similar. It will disappear in a flash. The member service section of the classifieds is a great place to start looking for restoration or honing services:
Member Services - Straight Razor Place Classifieds
There is a cigar store on Sainte Catherine called Vasco that has some quality soaps, etc. I'm pretty sure they also carry razors/brushes etc., but to be honest when I was there a while back I just had soap on the brain so I wasn't paying attention to the other stuff. :) Anyway, if you're downtown, it would be worth checking out.
Good luck!
EDIT: forgot to say - don't worry about having trouble under the chin. That's a very common trouble spot for a lot of guys, and will get easier with time and practice. If you search the forum, you'll find plenty of threads about that with lots of suggestions. But in short, prep well, stretch your skin, pay attention to your blade angle (raise the spine about two spine widths from your skin which should = an angle of around 30 degrees) and keep your pressure light.