My zlclient.exe is only using a little over 3.5 megs of memory. I have 1 GB of RAM. Unless you have an excessive amount of programs running, ZA should not slow your PC down. Use Task Manager to check the memory usage yourself.
If you are using IE and especially Firefox, check the memory usage for those two. I don't use IE, but I do know that if FF has been open for a long time, especially with lots of extensions installed, memory usage really gets to be very high. Just closing the browser restores memory to its normal value. I have monitored this myself.
If there are any other programs that may be using a lot of memory and you do not need them, do not shut them down from Task Manager, but use Start>Run and type in msconfig, click OK and go to Startup tab and uncheck the programs you do not need. Reboot as requested. Check box in lower-left corner on window that pops up after reboot and click OK.
Make sure ZA, when it installed, has turned your Windows Firewall off. You don't want both on. Zone Alarm is a lot better at Windows' firewall and you can run several security tests at GRC.com
to verify that.
I hope you do not have any anti-virus program like Norton/McAfee installed and running. These are the REAL resource hogs. verified on my sister's PC that only has 512MB of RAM. She has a PC that runs at the speed of a snail. Will not let me change it.