My climate is so different than yours, I'd be hesitant to offer a suggestion. You could always try asking Cindy at Hummingbird Farms in Maine, as I am guessing that your climate would be similar to hers, and she has been helpful in answering my clematis questions in the past. Hopefully others in a colder climate will add their thoughts.

Here is a link that might be useful: clematis at Hummingbird Farm in Turner, Maine

Keep in mind it can take three years or more after planting clematis to get a nice display of flowers. Some varieties take longer to mature than others. If you want a quick display you might consider planting morning glories instead of clematis.

There are so many variables, color, size of bloom, months of bloom, size of vine, size of trellis/arbor needed for three clematis, etc. You probably need some other supportive wire or strings as clematis need very thin rails to wrap around.

There are few really red or really blue clematis, most are shades of maroon or purple. Also differences in soil and sun can affect color of bloom. To make pruning easier it also helps if they are all the same pruning requirement though P:2 clematis can be pruned the same as P:3 clematis with the loss of early blooms.

You will want to do some research and serious thinking about your choices as the time and effort to achieve your goal is considerable. Clematis on The Web is a good site for researching.

For me in Z:4 some suggestions:
Red: Rebecca is bright red in some sunlight exposures and more scarlet/maroon in others P:2
Gravety Beauty, reddish P: 3

White: Huldine P:3
Lanuginosa Candida P: 2

Blue: Blue Angel P: 3
Kingfisher P:2

To help those of us that are not familiar with zip codes it would be helpful to use your zone instead.

I look forward to seeing your results.

As no one else answered you, Ive been looking at this idea too.I have found that you want to have them all blooming at the same time which can pose difficulties if you are just going by color. Size is important too. Some possibilites Ive come up with are

Red: I have this one and know how red it looks,
John Howells from Silver Star vinery
is a group3 and blooms midsummer through Sept for me is 8-10 ft

White: Maria Cornelia grp 3, small flowered(four petaled star shape) is said to bloom from mid summer through fall I dont have this it is supposed to be 8-10 ft
Blue: I find the darker violet clematis fill the job the best, Etoile Violette, or Romantika or even Galore but its color may not be the best for this. They are all type 3 and about 10 feet. and bloom more summer to fall
hope this helps and is not too late!
roseberri