Anxiety is not a requisite of shooting, and particularly not of shooting well.
As long as you remember the safety rules and carefully apply them, you'll be OK.
Here are the rules:
• Always treat every gun as if it were loaded and ready to do harm, even when you know that it's not.
• Never point any gun at something that you are not willing to destroy.
• Keep your finger off of the gun's trigger until you have it pointed in the right direction, and are actually ready to shoot something.
Guns that fire the .22 rimfire cartridge do not need to be detail-cleaned very often. Don't worry about taking yours apart.
Get a cleaning device called a "Boresnake," and use it to clean the bore of your pistol's barrel after every shooting session. You don't have to take the gun apart to do this, but rather only to latch its action open. Your instruction book will explain how to do that.
Use an old, dry toothbrush to clean any foreign material out of your pistol's "works" after every shooting session. You do not have to take the gun apart to do this.
Use little drops of oil to lubricate the parts of your gun which slide against each other. Use very little oil to do this. The brand of oil is not important.
Once a year, take your pistol to a gunsmith, and pay him to disassemble and detail-clean it.
Don't obsess. Just enjoy the learning experience.
It's only a mechanism. There isn't much you can do, that'll cause permanent harm to it.