Blaze is a good old standby climber, but the Iceberg I know is a floribunda, that only gets about 3-4 feet high, so not quite what you're looking for.
Scott has given you exactly what the low down is on cheapie versus more expensive roses. If you do decide to go with more expensive roses, you can still get them at a decent price. Don't think that the more you pay is necessarily getting you a better rose.
There are a number of good climbers out there, and also, because it is on a fence, you may want to consider ramblers. They tend to spread a little more, and have a longer, more flexible cane. Their flowering patterns are different however. A climber will bloom on it's main cane, and then send out lateral branches that will also bloom. A rambler will not bloom on a first year cane, but will bloom after that. You could also consider a mix.
Here are a few of each:
- Altissimo - red, 5" single petal flowers with a spread of 8 ft and height of 10-14 ft. Considered one of the easiest climbers to grow.
- Dublin Bay - red, 4.5" double blooms with a spread of 7 ft and height of 14 ft. Highly disease resistant and blooms longer than other climbers.
- Madame Alfred Carriere - white, 3" double blooms with a spread of 12 ft and height of 18 ft. Also a longlasting bloomer.
- City of York - white, semi-double blooms, with a spread of 12 ft and height of 20 ft. Disease resistant and vigourous grower.
- Adelaide d'Orleans - white, double blooms, with a spread of 10 ft and height of 15 ft. Does well even in poorer soils.
- Bobbie James - white, double blooms, with spread of 20 ft and height of up to 30 ft. Profuse bloomer.
- Chevy Chase - red, double blooms, with spread of 8 ft and height of 15 ft. Blooms in tight, full clusters.
Hope this all helps!