The flattest route, although parts of it can be quite boring, is to drive Hwy 5 from Jasper to Kamloops and then Hwy 1 to Vancouver. Use your transmission to slow you down on the hills rather than your brakes, which should be used sparingly to avoid overheating and fading.
You do need winter tires in BC, but the minimum requirement is for tires to be marked M+S, which most? truck tires already are? You do however, need full snow tires, marked with the 'Mountain & Snowflake' on the Icefields Parkway between Lake Louise and Jasper.
