I don't know what Ada wants to do; I don't think that was ever revealed. I do remember playing through 1 and 2 and noting that she was engaged to someone who worked for Umbrella simply to get information from him. In 4, she works for Wesker, but she says she is really for "the origination," who wants the plagas sample (and presumably the G-virus in 2). I'm not sure if the organization is good or not, but I always thought of Ada as the Catwoman of RE. At any rate, the villains needed a female, and I'm sure that's why they put her on the bad side.
"The Organization" sent a spy, Ada Wong (not her real name), to infiltrate the Arklay Research Facility. She started a fake relationship with John Clemens, the chief researcher at the laboratory, and managed to get information about the t-virus and Umbrella's BOW's. They contacted Albert Wesker in order to steal the combat data from the mansion incident. However, he wasn't able to hand them the Tyrant or it's combat data. The Organization then started their own BOW development.
To regain his reputation, Wesker planned to give the G-virus to The Organization. However, having faked his death in the mansion incident, he requests Ada's help. Ada failed to retrieve a sample but, minutes before Raccoon's destruction, she contacted Wesker revealing she managed to get a tissue sample from a G organism, containing the G-virus. Wesker saved Ada and handed the virus to The Organization (combat data from G and Nemesis-T Type were also recorded).
Wesker attacked the Rockfort Island using the HFC and retrieved Steve Burnside's body, containing the t-Alexia virus. BOW samples were also retrieved.
The Organization
In 2004, Wesker, now working with the "3rd Organization", hired Jack Krauser to work as a spy for Los Illuminados, kidnapping Ashley Graham for them, in order to steal a dominant plaga sample. However, he didn't have access to the sample so he asked for assistance. He invited Ada to join his secret organization, ordering her to retrieve the sample stolen by Luis Sera. She succeeded in retrieving the dominant plaga, but she sent it to The Organization, sending Wesker a subordinate plaga sample instead. However, Wesker managed to retrieve a dead dominant plaga through the body of Krauser.
Spencer, wishing to be met by Wesker, ordered his butler to give his location to Ada Wong. Ada, through Ricardo Irving, forwarded this information to Wesker.
After the Spencer Estate incident, Wesker dissolved the 3rd Organization, using it's resources in the Uroboros project he developed with the help of Tricell.
