Avast and MalwareBytes work against different nasties. Definitely keep both.
If you have Windows 7 or 8, I believe the Windows Firewall is fine.
Having said all that, I strongly believe that just about THE most important anti-malware program is SpywareBlaster. It stops malware from entering your machine, whereas MalwareBytes Free can only find the nasties after they are already in place.
SpywareBlaster is non-intrusive and doesn't need to run in background. All you have to do is check for and install updates regularly (usually about once a week). It doesn't interfere with any other program. I simply wouldn't be without it on any Windows PC.
https://www.brightfort.com/spywareblaster.html