I don't think one variety of a bean/carrot/pea as opposed to another makes a difference when it comes to soil. My soil is also alkaline and vegetables grow fine.

What you do want to pay attention to, however, is days to maturity and choose those with early maturity dates. For example, choose a variety of carrot that matures in say 65 days rather than 85 days.

Since you're in zone 3 you might also want to check out the very active Far North forum here on Gardenweb. If you ask your question there, some people may be able to recommend specific varieties of seed.

Here is a link that might be useful: far north forum