Jonn, I'm going to suggest you stick with a factory airplane for your first, unless you have some very good, close friends who can help you manage and maintain a homebuilt. If you're the do-it-yourself type with lots of experience with engines, structures, etc, then a homebuilt might work, but it will be a lot easier to find correct parts and mechanics knowledgeable about a factory plane.
There's going to be a lot to learn just managing and maintaining a Cessna or Piper, but you can always pay someone to do much of it. Example, annual inspection time comes, I order the parts and filters and batteries I know I'll need. You can't just call Aircraft Spruce and say "I need plugs, oil, air and vacuum filters for an RV-9. They won't have any idea, depends on how it was built, what engine was installed, etc.
For your "mission" as you have described it, I'd suggest a Piper Archer. Find one with up-to-date radios, nav gear, and working autopilot. Reasonable cruise speed, and power to get you over the California mountains in NICE weather. I wouldn't fool with the mountains in bad weather in any plane we're discussing. I myself own a C172, but the Archer is a bit nicer instrument platform IMHO. I did a lot of instrument instructing in Cherokee 180s and Archers, and they are just a little heavier and aren't as bothered by light turbulence. MAKE SURE you get a good pre-buy inspection by an independent mechanic who has nothing to do with the seller!
The C182 is also a good instrument platform, and is easier to get in-out of, rather than everyone having to enter/exit a single door over the wing. But it's more complex with a controllable-pitch prop and more than double your target fuel burn.
Cessna's and Pipers are going to be easiest to find parts and service for. Grummans are fine, as is the Beech Sundowner, but not nearly as common or easy to find airframe parts for.
After you've earned the instrument ticket, accumulated around 400 hours, and been through 3-4 annual inspections and maintenance surprises with your first airplane, then you can start thinking about sexier, faster, more efficient, etc. and easily peddle or trade your Cessna or Piper.