As I've never actually travelled to Europe (living in California makes trips to Mexico and Hawa'ii just too easy) I am at a loss as to how best to get her there without going broke

When I look for non-stop flights from San Francisco to Helsinki, the prices are (at least to me) exhorbitant ($1,400 - $1,500 USD). But it does seem that flying from SFO to London, for example, is reasonable and then flights from London to Helsinki aren't so expensive.
Is this what most people do? If yes, what is a good, safe airline to fly from London to Helsinki?
Thank you for any suggestions.
Mrs. Hourula