What is the best program to work as a virtual assistant?
Congratulations on taking the time to choose your technology wisely!
The best thing is for you to use some sort of online project management software. Basecamp is a good option: http://www.basecamphq.com or http://www.wrike.com has a more user-friendly interface.
As for accessing your clients' e-mail, that depends on what e-mail software they use. Most people use Outlook, in which case, it might make sense for you to recommend a hosted Outlook solution, which would allow you to create your own e-mail address like Roxxy@clientcompany.com so that your client support is seamless and invisible to outsiders. A hosted Outlook setup also allows you to manage and reconcile your client's calendars. Most major hosting companies offer this service.
A good company for hosted Outlook services is: http://www.123together.com/. It even offers a 30-day trial of the software. That's always a good thing.
However, before you use a service like this, make sure that your client's hosting company doesn't already offer it for a nominal investment.