You can add both your incoming and outgoing email information to gmail if you want to stick to using Google Gmail as your webmail service.
To setup your Incoming(POP) email in Gmail please use the following article:
https://support.google.com/mail/answer/21289?hl=en
Use the section that says "A different provider"
To setup your Outgoing(SMTP) email in Gmail please use the following article
https://support.google.com/mail/answer/22370?hl=en
Use the section that says "Im a Gmail or Google Apps user sending from an external address"
For POP settings use:
hostname: (Found in your welcome email)
Port: 995
Check the box: "Always use a secure connection (SSL) when retrieving mail."
For SMTP settings use:
hostname: (Found in your welcome email)
Port: 587
Fill in the dot for: "Secured connection using TLS"
If you need any assistance in the process please feel free to open a ticket.