Don't know if i've misread your question but do you only want to plant 3 plants (climbers) to cover 100 feet.....or do you want to just plant 3 types of climber (but lots of them.)
For the first scenario....only wanting to plant 3 plants, i'd go for clematis montana, clematis armandii and hedera canariensis....all these are rampant and by planting just 3 plants, will more than likely cover thew fence in 10 years
For the second scenario......3 species of climber but planting lots of that species, i'd go for Trachelospermum jasminoides, Pyrecantha and Actinidia kolomikta (the last being deciduous)