Profile as in a Social Network Site
You can control how the user is redirected after login using the Rules module.  Create a rule using the event User logs in and action Redirect to page.  You can create as many redirect rules as you need to get the user to go to the appropriate destination.

For example, for my social networking site, I do the following:


redirect users who haven't completed their profiles to a page telling them they need to do that (condition: user doesn't have profile_completed role)
redirect users who have completed their profiles and have new messages (from private message module) to the message inbox (condition: custom PHP condition)
redirect all other users to the search screen


In my implementation, I actually implemented this as a rule set (component) instead of a bunch of individual rules so that I could easily achieve the third option ("redirect all other users").