Time Machine Question

When I installed Mountain Lion, I did a clean install and started all over fresh with a new user. On Lion, I had Time Machine set-up and everything backed up. So when Mountain Lion was installed, I just moved what I wanted over.

Still, a few weeks after Mountain Lion, I still find that I need to go into my "old Mac" to move something over.

Is there a way to delete all but the last backup? If I understand Time Machine correctly, it doesn't do a full backup every time, just the changes made. So if I delete all but the last backup, it'll only save the stuff moved over in that backup.

I want to get Time Machine running again on this "new" Mac. But I want to save the last backup on the "old" machine. What can I do to achieve this?