Yes basecamp would be good. It's user-friendly interface makes it easy for people to use and aside from that, it's also cheap. Another great software I can recommend is Zoho Projects. It got a lot of features aside from the basic ones like time tracking, document/file sharing, etc. If you are confused of which project management software to use, you can read reviews of them found in blogs or forums.

It would be great too if you can find a comparison table of the various project management software which are the most popular nowadays being compared by each other and also where you could also see what features the software can offer.