Most modern hybrid impatiens bloom adequately, and lack of blooms tend to be due to horticultural problems rather than cultivar selection.
cultivars which has done great for us: accent, tempo, super elfin, mosaic, etc
Use little or no fertilizer in starting medium.
Fertilize impatiens very lightly as seedlings, but do remember to fertilize them. Seedlings which did not receive any fertilizer young, flowers poorly later.
use a low phosphorus, high nitrate fertilizer during seedling stage to provide good compact growth. high ammonium levels tend to stress plants and reduce branching.

You can take cuttings of those that bloom well and grow them indoors by the window sill till next spring.

I like super elfin. They don't get leggy and are very full. Just mho though!!

I have had great luck with the accent series. I use fertilizer every other week. 15-30-15