You were right to get rid of mse, see this article:
http://www.informationweek.com/security/antivirus/microsoft-security-essentials-loses-av-c/240142986
Now, on to avg....No, it is not that great of an AV program. While for 2013 their virus definitions database has improved, it is the only tool it uses to protect a computer, and in today's malware world, that is not enough to protect a computer.
Since you already paid for it, you should use it until the license expires, but I would also get MalwareBytes pro to help protect your computer. It is only 25 dollars U.S. for a lifetime license.
When your license expires, you should get one of these AV programs, they are the top AV products, and score very high in testing every year.
BitDefender.
GData.
Kaspersky.
You won't go wrong with any of those, and with MalwareBytes pro, you will have excellent protection.
Good luck.