Transfer selected folders from Time Machine

Can I transfer selected folders from Time Machine to the hard drive in my new Mac Mini? I don't want to restore the entire backed up hard drive. I want to keep all the files but don't need them all so I'd like to leave some on the backup drive.

For example, how do I transfer all my Mail messages from the old computer to the new one? Can I drag the Mail folders onto a thumb drive, then drag them onto my new computer? Same with my photos.

There are other programs I've purchased, like Quicken Essentials and Tube Sock, that I want to use on the new MM. I don't think I should have to buy them again just because I have upgraded my computer but I don't know how to get them off one computer and onto the other.

I bought a second external hard drive to backup the new MM because presumably, if I don't and I delete everything on my old MM hard drive, the first backup from the new MM will overwrite the last one from the old MM.

I thought I'd keep the old external backup drive for everything on the old MM and the new external hard drive to start fresh with the new MM

Does any of this make sense?!

Thank you.