To add to my previous reply...I added those I wanted to keep on my new account as friends. I ended up unfriending them on the old account because having mutual friends was causing my new account to pop up as "someone you may" know on my old account and vice versa. When I created my new accounts I wasn't full time yet, so that also contributed to choosing the new account route.
I'm still trying to figure out what to do with Google. I could either create a new account or just unfriend a couple people and change the name and picture. The problem is 1) I used that account to buy Apps in the Play Store, etc...so creating a new account would mean having to buy everything again, and 2) While I can unfriend and change my name and picture, I cannot change the email (gmail) address associated with the account like I was able to do with Facebook (preventing anyone from finding me by my old email address). Personally, this isn't too much of an issue as I never really used Google+, but I hate seeing the old picture/name every time I access any Google sites, such as Google Calendar.