Welcome! It's a whole 'nuther world down here!
The only vine that will stick to the wall by itself in full or afternoon sun is cat's claw. It has good features, but beware: think aggressive, invasive, and immortal.

I don't know about 'Frederick', but most varieties of Passiflora edulis are extremely frost tender.

Hardenbergia needs shade in the afternoon, and special soil and watering even there.

What kind of honeysuckle? There are several vines available called honeysuckle, with different needs and features.

Snapdragon vine is primarily a frost tender annual here in the Valley, and even more so in the rest of the state.

What kind of trumpet vine? Again, there are several of 'em.

Look for vines in the Sunset Western Garden Book suitable for the Sunset zone of your area. The USDA and Arnold Arboretum climate zones aren't worth much west of the Pecos: there's a world of difference between between southern Arizona zone 9, and coastal Washington state zone 9! The Sunset zones are indicative of the other major climatic factors in the area, as well as winter lows.

Also, check with Certified Nursery Professionals and/or AZ Master Gardeners in your area. They've had the training and experience with growing things in this climate. Others may know what they are talking about, but some are going to be recent immigrants from Virginia or L.A., and only think they know.

My favorites for a sunny wall?
Snail vine (Vigna caracalla), pink trumpet vine (Podranea ricasoliana), yellow or lilac orchid vine (Mascagnia species), Cape honeysuckle (Tecoma capensis), and hacienda creeper (Parthenocissus, unknown species*)
*Be sure to get hacienda creeper--Virginia creeper and Boston ivy are both also Parthenocissus, but they both need shade everywhere under 4000 ft. elevation!

Happy hunting! : ])

Thank you guys so much! I am really excited to get started. I'm making a list of all your suggestions and heading to the nursery this weekend :-) I'm so glad I found this site!

I'm curious what others would have to say about using plants like the climbing fig? (Ficus Pumila) I even understand that there's a new one out there, that is edible (Ficus Pumila x carica) I've seen them climb on fences and walls with no problem and they look beautiful and they don't mind the heat at all. Are they really bad?

I like climbing fig, though it can really struggle on a hot sunny wall. I see it used to great effect on shady walls. When it's young it makes the tiny juvenile foliage but when it's mature it makes larger (sort of orange tree leaf sized) leaves which are still very nice, and it makes interesting egg-sized fruit. I love it and it does climb on its own, but it seems to burn a lot in summer sun. Let's see what everyone else says too.

M-with-a-plan, if you end up putting up a trellis or those vine-holders you'll have a lot of options as you see. I love all of the ideas and comments tugbrethill posted. Let us know what you do and how it works out.

Take care,
Grant

I have a harbenbergia on the north side wall of my side yard it is on a trellis the trunk starts under a mesquite tree and the plant stretches almost 30 ft!! I love it, in Feb the entire vine is purple and the side yard smell great

Calb sent me a pic of her hardenbergia--I'm impressive! I'm embedding it below and putting a link too. I really do like them for partially or fully shaded walls. Lookin' good!

Calb_gardner's Hardenbergia ("lilac vine")

{{gwi:422201}}

Happy gardening everyone,
Grant

Here is a link that might be useful: Calb_gardner's lilac vine

Right by my front door is a block wall
It gets a lot of sun how much, and is it morning, afternoon or all day?
prefer not to put up a trellis

None of the vines on your list can fill that spot very well with those stipulations. Cat's Claw could cover the wall without a trellis, and then start covering the front door and the house. The others need a trellis or can't handle "a lot of sun" or both.

One way to handle the problem is to plant the vine on the shady side of a wall, with a trellis or vine holders, and let it trail over the wall onto the sunny side. It increases your choices. Yellow Orchid vine does well like that http://www.desert-tropicals.com/Plants/Malpighiaceae/Mascagnia_macroptera.html

How big is the space? Could it handle a tall vertical-growing shrub or a small tree like a desert willow?

Lazy, I need to say, your idea of deliberately planting the vine on the "other side" of a wall is excellent! I've seen it a million times (especially with cat's claw as I mentioned above): a vine looks leggy on the side it was planted and lush on the side it trailed over, but I never really thought about doing that on PURPOSE. Great idea--I'm glad you mentioned it.

On a related note, a friend of mine in N. Phoenix bought a house where the neighbor's cat claw vine had grown up and over onto my friend's side and it was a beautiful, lush, green "hedge" effect--that is, until the neighbors sold and the new folks cut each vine off at the base and left my friend to deal with the suddenly-dead tops. Ugh. Anyway, when we own both sides of the wall, it's a great idea. I'm going to give it a try myself.

Take care and happy gardening everyone,
Grant

Does anyone know if cats claws roots destroy pool lines and irrigation system tubes? I would like to plant it to cover two sun exposed walls of the garden but there are lines everywhere under the ground level.

>> ...anyone know if cats claws roots destroy pool lines and
>> irrigation system tubes?

The roots are little hairy things leading to a big fat tuber. The vines come off the tuber. Other than tree roots inside of some cracked fifty year old cast iron waste lines, I have never seen any root invasions from anything, and I have a lot of cat claw and a lot of creeping fig.

Thank you very much.
I planted five plants and they took off like crazy. But then yesterday i accidentally found reviews on CC and they were so bad. I was biting myself for planting them! :) I assume it makes a lot of damage in hot humid climate but hopefully here it is a slightly different story.
May I also ask you a few questions?
I also planted english ivy but it grows horizontally for some reason. In a battle between ivy and CC, which do you think will eventually take over?
I have a lemon tree next to the wall where CC is growing. Will CC damage lemon's roots?

Thank you!