Wondering the tradeoffs of inheriting time machine backup

I just added a new 15" MacBook Air as my primary machine. My older MacBook Pro (2013 edition) will remain in the rotation as a backup machine with partial usage. Using migration assistant I moved my user account, and it offered to pickup my Time Machine backups. While this generally makes sense to accept, I want to understand the ins and outs.

While I have migrated my user account, one thing I have NOT migrated yet is my large photo library from Aperture (which was on a separate drive). This will need to transition to Lightroom at some point, and I'm not taking that project on immediately. Backing up photos is one my main needs, so the fact that I haven't migrated that library yet makes me think I should wait to inherently the TM backup. So my questions:

1. If I'm migrating my account and primary usage (I am) is there any argue to start a new TM backup rather than inherent the older old?
2. Can I delay inheriting until after I handle the photo library in the next few weeks? How would I trigger this when ready?
3. If I inherent, will the old machine then start its own set of new backups? That would make for a lot of redundant data usage on my TM drive as they have all the same files (outside of the photos). I did intent to leave the old machine frozen in time to have a backup of a lot of key documents (in addition to TM that is)

Thanks support forums - I just can't seem to find much information on what happens to the old machine if I choose to inherent, and to be honest while I've backed up for years, I've never actually used Time Machine to restore so I'm not particular familar with it.