When setting up a new website, how important is it to include keywords and potential search terms in the actual domain name? How heavily is this weighted when it comes to ranking highly on google searches?
You're not going to get an exact answer as no one knows exactly how much weight those keywords carry except Google. We do know that they currently carry lot of value but we also know that Google is working on reducing it.
To add to what John Conde said...
It used to be a ticket to the top but over the past 18 months or so it's been blunted a good bit when it comes to many generic keywords. Google wanted to prevent quick buck artists from buying something like greentennisshoes.com, stuffing it with affiliate ads and rocketing to the top of search results nearly automatically.
In its place, they've begun to rely more on "brand" signals and geo-location signals to filter results, especially on searches for commercial terms. This means that if I look for green tennis shoes I'm probably going to see results from Amazon, Sears and other major retailers as well as local shoe stores (if there are any and depending on if I'm using mobile search or not) rather than a thin affiliate exact keyword match domain.