Some come in, and some don't

Hi,
I downloaded the 2013 Office plus Outlook and have been trying to have a positive attitude about learning the new stuff.
Here is my problem....got all my different email accounts set up correctly (got the congratulatory window after testing) and imported my contacts correctly. But not all my emails come through.
Here is how I know -- I still have my old PC running, hedging my bets. I can't afford to lose business because I'm learning! The settings are for the emails to stay on the server, so I get all the emails on my old pc, and then on the new pc as well. NOT. Only some of them come in on the new.
I checked the junk folder to see if it was because of aggressive filtering, but there was nothing there.
All of the tutorials I have watched mentioned that if you had a message come from someone in your contact list, it would land in your inbox......mine don't ALL land there.
Does this sound familiar to anyone? Can you help me?
I sure would appreciate it!