I just moved from iPhone to a Galaxy S4, and I'm trying to get it set up. I have a gmail account, and two NON-gmail accounts. What is the best solution to have all of my emails managed in one place/app? I would really prefer not having to switch between two apps to check my emails if possible. Thanks for any assistance.
This official Google support page tells you how to access Gmail from a normal email client using IMAP: you have to turn it on through the Gmail web interface, then add the account to your email client like any other IMAP server.
The standard email client on Samsung devices supports having multiple accounts. Press the + button in the Email app's settings to add an additional account. Most third-party email clients for Android (such as K9-Mail) support multiple accounts too, but the set-up will be slightly different for each.