Hi,
From what you have mentioned, i guess you need to have your own email address on your domain, something like
yourname@yournewdomain.com .. if yes, then you have multiple options.

1) Use a third party email hosting service:
Yes, it is very good to use third party service, because it saves you from the overhead of managing your email server.

The good options include: a) Zoho Mail ( https://www.zoho.com/mail/ ) - Free
b) Gmail (Paid )

In Both the cases you need to point your MX Records to their servers, which can be easily done and take very small time.

2) Installing Email on Same server:
Well in your case just to save extra overhead i would not recommend it, however if at all you want to go ahead and have something alike, you need to install MTA on your server.

Depending on your server there are set of simple commands that istall the mail server :-)

You can also install PostFix.

Some good tutorials you want to read :

https://www.digitalocean.com/community/tutorials/how-to-install-and-setup-postfix-on-ubuntu-12-04

Again, the best way is to just go ahead to zoho, create the email and point your mx records. thats it..
happy mailing .