There are quite a lot of red climbing roses. What would be best for you depends on the space you have available for it.

I myself grow Cl. Etoile de Hollande and Sympathie. Both are very different. Etoile is velvety red and 'blues' in the sun so the flowers become velvety purple and this is kinda nice, but you have to like it. It is very fragrant. Sympathie's red is of much higher quality. It is a good red and it stays red even in the heat wave temperatures we have currently. It has only a light scent. Both roses are vigorous and tend to become leggy, so they are, I think, best against a wall and not for a pillar (like I grow them). I saw the Etoile in France covering a wall and it was like 4 m. high.

Other red climbers that I do not grow are Santana, from Tantau, relatively new (1985) and probably healthy, not fragrant and good for a pillar spot. Amadeus, a new Kordes climber (2004), light fragrance, very glossy foliage and probably very disease resistant. The flowers seem to be semi-double and very red. I think you have to order it from Kordes. Santana is available in garden centres here.

Older favourites are Don Juan, a classic climber with hybrid tea like flowers, and Altissimo, a red with single flowers. I don't know how they do in the resistance department. Other resistant classics are Dortmund (single flowers) and Parkdirektor Riggers (semi-double) but they both lack scent. Both are from Kordes and related to Sympathie (all three are so-called Kordesii-hybrids).

Oh yes, then there is Red Eden Rose (or Eric Tabarly) with old-fashioned type of flowers and some scent (not very strong, even though advertised as such). It's new from Meilland (2004) and I have mixed feelings. The flowers are nice (raspberry red), but a bit overhyped and they tend to be damaged by rain and foggy mornings. It's still healthy though.

The rose you see most in the garden centre, often without it's name, is Paul's Scarlet Climber. I do not grow it but I believe it has long been surpassed by better varieties.

The above roses are modern roses that repeat flower. Generally, though, the shorter the rose stays the better it repeats. Santana and Amadeus are probably best for repeat, because they tend to stay shorter. You may also opt for once blooming varieties although I don't know wether there are pure reds in that category. Excelsa comes to mind, or maybe Super Excelsa, a repeat flowering child of Excelsa and more disease resistant.

Last, but not least, roses need a lot of sun and good airflow. I grow many roses in good spots and they do not get disease. However, the roses in my parent's garden get disease easily because they are planted in a small garden with fences (schutting) all around and trees blocking the sun. So, with respect to health, your mileage may vary.

Hope I was of help :-)
Rob