This question is only relevant if your company name is not available in the dot com TLD (top level domain) realm. For example your company name is XYZ, but there's an XYZ on the other side of the world who snatched it up first. In this case you will be looking to expand on the name with a relevant keyword. The primary concern here should be keyword relevance.
If you still draw blanks or unavailable names, then you can go with the less desireable.
You might consider using just a keyword domain (ie. WidgetSolutions.com), however in the long term I would recommend against it for your marketable domain name. Your company name is your brand, and you should make sure consumers hear it and see it as often as possible.
Tip : Don't consider XYZ.org or XYZ.net as your "go to" domain name. You'll immediately lead a large portion of users to a possibly competing website because dot com is so ingrained. (You may want to register and redirect similar domains to your final choice, but its not something you'd put in your marketing materials and promote.)
Tip : At all costs, avoid dashes or other non-alphanumeric characters. They do not speak well, and lead to a constant need to spell out your domain on the phone and when someone wants your email address.
Tip : If you have a trademarked company name, and the current domain name owner is not using it for any well intentioned purpose you may have a shot at blocking their use and getting it transferred. (consult a lawyer)
Once you've decided on your domain, register it for free here.
Just remember -- A great name can be a head start, but it won't get you to the finish line. A name is very important, but not if it keeps you from ever getting your business online. Moving your business from local to an international customer base can open streams of revenue you previously might not have imagined. In the end the most important thing is your business model and the execution of that business model.
Don't forget many great websites start from a pre-existing business, and become businesses all on their own. If you might consider your website a whole new business read How to Choose a Domain Name for a Startup Business Website.