Don't buy snow tires for one outing, especially if you're not driving in snow 100% of the time, they will wear quickly and a waste of money for a trip to the mountains.
One thing you will want to check is to see how much clearance you have around your tires, make sure if the suspension flexes that the chains will not hit the body or frame at full lock, the diagonal cable chains are better for this as they are lower profile than the larger chain chains. You also must account for centrifugal force pulling the chains away from the tires at speed, so just because the chains clear when at a stand still does not mean they won't hit the fenders at 20mph.
And like Ghost said, with M+S tires, 9 times out of 10, you will not need to put on your chains at any checkpoint, just have them in the vehicle. I have only been asked by CHP if I had chains once, most of the time they don't even make me stop.
Don't use lockers on the street with snow, but 4hi helps. Offroad, lockers can help if you're stuck but they shouldn't be used unless needed honestly.
Chains go on the main drive tires, meaning rear wheels for RWD/4WD, front wheels for FWD vehicles(most cars, vans and SUV sadly). If the ice conditions are really bad, chains on all 4 tires can be done but honestly, you just shouldn't be driving at that point unless it's a serious emergency.