Been about a year since I removed SpywareTerminator. It's a fairly good program, the HIPS component- whilst taking a bit of learning about- providing a good additional layer of security.
If you don't like, or don't know how to, answer popups on many aspects of computer behaviour, don't integrate the HIPS. I would also not recommend the toolbar or the Clam AV, but that's down to personal choice.
AdAware will never see my computer again. Buggy, bloated, ineffective, and with poor support, is how I found it, after SE was discontinued.
What I'd recommend would be a few standalone apps or settings that can run beside Avast and "plug any gaps", as it were.
Such things would include a behaviour blocker, such as, say, Threatfire, a two way firewall, and some browser immunity, which might include a Hosts file, and/or SpywareBlaster, disabling or prompting for the running of scripts in the browser (eg Firefox with the Noscript extension), and some folk also recommend running the apps that connect to the web (browser, p2p etc) with reduced privileges. (Google "dropmyrights")
I would also recommend trying out a few of the tools that offer such protections, be it SpywareTerminator, AdAware, Boclean etc, and see how they all run together, how the support (if needed) is, what the protection is like etc.
Some apps run brilliantly on some computers, and not at all well on differently set-up systems. (Example: I'd be very keen to try OA firewall, have done three times, my computer dies with it installed. Too hard to troubleshoot it at the (non) speed it runs at, despite willingness on the part of the company to help. Most other users have very good experiences with it.)