One option: use the Due Date rather than the Start Date. To hide a task with a Due Date more than a week away, select View-Current View-Next Seven Days - but don't enter separate Start and Due dates, or you may be reminded to do something too late.
Another option, and the only one that actually understands the concept of a start date, is View-Current View-Task Timeline. This will give you an entirely different view of your tasks - one where each task marks or blocks out the space between its Start Date and its Due Date.
If you use Outlook 98 or 2000, you may want to alter your Outlook Today view as well. Go to Outlook Today. Then in Outlook 98, click Options; or in Outlook 2000, click Customize Outlook Today. In the Tasks section, for "In my task list, show me", select Today's tasks. Click Save Changes. (But remember, Microsoft assumes "Today's tasks" are those due today, not starting today. Oh, well.)