dgkiwi,
Avast is an antivirus program only. However, it can check email for viruses and it's the best one I've ever tried for this.
Therefore, you will need a firewall and a spam checker also. I use eTrust EZ Firewall 3.7.211 (free for 1 year) and SpamPal 1.53 (freeware).
I know that you'll probably get more suggestions for firewalls and spam checkers. But, I've used quite a few of the free ones and have settled for the ones I recommend.