. . .
Once complete, can I restore the things I need from the most recent Time Machine backup?
If you mean 3rd-party apps, individually, in some cases yes, in others, no.
See Transferring Applications for an explanation.
I also plan to do a manual copy of the data files I need.
If you mean drag & drop from Time Machine backups, that's problematical, especially if you have non-standard permissions, such as for multiple users. Your best bet is probably to use the "Star Wars" display, per #15 in Time Machine - Frequently Asked Questions.