Perennial or annual?

Perennial, sorry.

I should say that I have several clematis and though I love the flowers, I don't appreciate how much I have to guide them and tie them on their supports. It seems I always miss that window in the Spring, and before I know it, they are all tangled and in a mangled bush at the bottom of the trellis. I'm hoping I can find something that will find its way up a bit more easier, without my help. This might be unrealistic, but I'm hopeful.

I think the clematis issue relates to it being the wrong kind of trellis, but that is easily fixed. Most clematis climb by twining their leaf stems (petioles) around things, and since the petioles are short, unless the support is pencil thickness or smaller, they can't twist around the support. You can put a piece of large-spaced wire mesh in front of the trellis or tie strings up it or drape a piece of netting (biodegradable if it's a hard prune, nylon or some other longer lived material if it's light or no prune since it's tough to separate the vines from the netting). Or plant your clematis where they will grow up the center of an obelisk. Do you know what type yours are? There are a few that don't climb but only a couple of them are available from regular (rather than specialty) nurseries, including Roguchi and Arabella.

Other than the smaller clematis, IME most vines that are perennial are fairly large - the native trumpet honeysuckle (Lonicera sempervirens), virginia creeper (Parthenocissus quinquefolia), and climbing hydrangea all require solid supports.

Babs-you're right about my supports for my clematis vines. I planted Arabella on either side of an arbor and tie it up each year and curse myself, since I should have just planted it in the garden bed as a ground cover. The other three clematis are: Guernsey Cream, Blue Ice, and Franziska Maria. I will take your tips and try to alter my supports to help them climb better on their own. As for my other arbor, I'm really hoping to plant something else besides clematis, but just don't know what. Here is a picture of it. I may try to stake it in the ground different to fortify it more. As you can see it is leaning onto my fence a bit after the first winter in the garden. That is why I called it "wonky".

Forgot to mention all are group 2, except Arabella which is 3.

Get some obelisks for Arabella to grow up the middle of. Here is my C. Star River (another nonvining C. integrifolia hybrid) growing up the center of a rose obelisk. I occasionally tuck the growing tips in as it grows but I don't tie at all. I think with an obelisk that had more wires I wouldn't even need to tuck in - this one is more like a tall plant ring. Also, they make plant clips that are a whole lot easier than tying.

I would plan to reinforce the wood tellis. I generally use 3'-4' pieces of rebar pounded into the ground at least a foot alongside the upright tellis members and fastened solidly in several places with zip ties of a similar color. I find that often the tellis legs aren't long enough to hold it solidly, especially in the wind once covered in vines.

That spot looks fairly shady. Is it? I think if it is, I can't think of any shade-loving, flowering vines that would grow there. Climbing Hydrangea is way too large for the site and needs a flat surface such as a masonry wall or tree trunk. If the spot has at least 4-5 hours of sun, consider some of the more shade-tolerant clematis.

If it's sunny, clematis or one of the really hardy climbing roses, though that will need to be clipped to the trellis. I have been successful with Zephirine Drouhin which is virtually thornless, so good for near where folks walk; don't use a thorny rose like New Dawn. I use clips to fasten ZD to the trellis. You could try Lonicera sempervirens, the native trumpet honeysuckle if there is at least a half day of sun, and there are some other non-invasive, hardy honeysuckles such as Mandarin. But all are stout, heavy vines and need a solid support.

If it is sunny you could also plant annual vines - scarlet runner beans, black-eyed Susan vine/Thunbergia, or morning glories.

One comment that I realize you haven't asked for - the color of the arched trellis is a marked contrast to the fence. If it were mine, I would get black wood stain to darken it so that it matches better and blends better with the fence once covered with vines.

Babs-you have given me much to think over, thanks for the help. The site is full sun all day actually. I took that photo at night. The arbor matched the fence before it was replaced, but that does make sense, now that you mention it-even when the cedar fades, it still may not look good. Perhaps, I will stain it, before growing something there. I'm going to look over all your vine suggestions-thanks so much.