Resident Evil 2 starts out with Leon S. Kennedy (the protaganist of RE4) sleeping in, just avoiding being in the middleof the outbreak.
He meets up with Claire Redfield until they are seperated from each other when an 18 Wheeler careers into Leon's police car.
From then on, we meet H.U.N.K, Umbrella's Special Forces operative trying to recover a sample of the G-Virus.
To not spoil the game, I leave it there.