17's on a 1962 Valiant Wagon

I think that wagon would look AWESOME with the right set of 17's. :D

I think 17's are about perfect for most of the 60's and 70's musclecars. You can still get enough sidewall that it doesn't look like you're running rubber bands, and the added diameter actually lets you run more backspace (tie rod ends fit inside the lip of the rim) so you can run wider tires and more modern compounds and tread designs so that you can actually improve handling A LOT.

Dan does have a point about the steering parts, although I personally think almost all of the steering parts are plenty strong enough once you get past the '67 design idlers, the 67 and earlier idlers were pretty much maxed out stock being set up in single shear and all. 9/16" tie rod ends are just fine, although tubular tie rods are a good idea vs the C channel stockers.

I run my Challenger with 275/40/17's, with all the stock steering parts including the c-channel tie rods, and haven't had any issues so far. I'm sure a set of tubular tie rods and new ends would tighten things up though.

Braking is definitely something to consider running larger rims and tires. You'll probably be adding some rotating mass, especially if you're going to run wider tires. The larger rims give you more space to run larger rotors too, and the additional traction means you can put more braking force to the ground as well. I run the LBP 11 3/4" rotors off the later mopars, and 11" rear drums. Fills up those big rims better, and really gives you some extra whoa power.