As a disclaimer, I don't know anything about alaska flying.
But for pretty much any job, where you get your private pilot license doesn't matter at all. 172's and Archers are solid aircraft. Usually small schools are cheaper. Learning in old planes is fine as long as they are well-maintained (many are), and I would say even better because you usually don't have the crutches like glass cockpits, nice GPS's, autopilots, etc. If you are going to Alaska I would think they're flying a ton of older stuff, so probably a good idea to stay away from glass cockpits until you are instrument rated. IMO, its always easier to transition from a six-pack to glass than the other way. For private pilot you are much better off flying a 20-30 year old PA-28 or 172 for $100-110/hour than a new one for $150/hour.
Like some people said, part-time CFI's can be hard to schedule, so see what their availability is before you get started. As for old instructors, they are like new instructors, some are good some are bad. Some are stuck in their old ways and have developed tons of bad habits, some are a wealth of knowledge.