The Twitter API and PHP - Best way to display Tweets

I have no experience with twitter other than using it and I can’t figure out if I need the Twitter API to accomplish this or just using a generic user search and jQuery. My platform is PHP can someone give me a brief roadmap how to accomplish the following tasks…

page 1 (a widget)
pull latest 5 tweets given a list of users (Moe, Curly and Larry)
— this will never work because 50 tweets will happen before the “last 5” ever get back but thats what the client wants
— this will display full name of the user
— this will display the date/time
— this will contain a link to view all from last 24 hours

page 2 (after clicking view all) - the last 24 hours of our users page
sorted newest first
Paginated @ 50 tweets per page

Moe says

  • tweet one

Curly says

  • tweet one

Moe says

  • tweet two

Larry says

  • tweet one

Do I need the API to accomplish this? Any thoughts ideas greatly appreciated.