You are in charge of optimisation, if you only have 512MB of RAM then you need to optimize what you run on startup and leave running in the background.
You don't say what your OS is which is crucial, XP has a recommended minimum of 256MB just to run it, leaving 256 for all the rest, your browser, email client, firewall and security applications. This cripples your system performance as the RAM is constantly being swapped out to the virtual memory (pagefile.sys) on your hard disk. The hard disk then is a bottle neck as it is much slower than working completely in RAM.
If you have Vista you are lucky if it will run at all on 512MB of RAM.
So essentially you should only have system and essential applications run on boot. avast by comparison to many other AVs is relatively light on resources.