I have been using Avast for a while but I have the basic Comodo firewall installed also on the computer I am using right now. Its a pretty old computer and doesnt have a big drive or allot of memory, so I am wondering if I can use Avast Home Edition 4.8.1335.90319(new) by itself now or do I still need to run a firewall?
I believe everyone should use a firewall and it’s good idea to turn on your firewall feature of modem. I advice you use PC Tools Firewall Plus instead of Comodo. It’s very easy and lightweight software . i like it a lot 
Avast never had a built in firewall nor acted or had any fireall capabilities till now so it very strongly advisable to install a firewall software.Sugestions may differ from your type of surfing and the sort of knoledge you have in this area. So asuming that you have a little knowledge you will be just fine with either of these
Zone Alarm free Firewall
PcTOOLS Firewall Plus free
Both are easy and there is a little intervienence needed .Otherwise if you know something about firewalls go ahead and use Comodo firewall or OnlineArmor free firewall