Hi Carol
I've moved your post here because it's likely to get more attention in this location which is specially for support requests.
I'm a little confused because first you talk about Comodo alerts (which I'm assuming relates to the firewall?) and then Avast! which is of course an AV solution. One comment I would make about the firewall is that it depends on how you answer the alerts which enables Comodo to remember your decision or not. If you choose the plain "allow" option then it will keep asking you the same questions.
What I would suggest please if I may to start with is that you have a browse through the article I wrote here because it isn't just the security programs on their own which will provide you with a safe environment online.
http://www.techsupportalert.com/cont...under-hour.htm
This might help you to decide what you think might be best for your own requirements, then you can post back here again for any advice you might need about setting it all up.