Welcome to THR, this is the best place to talk firearms and related
topics. The people here are most cool and helpful.
I've posted several links for you, the first below is to "LAX Firing Range"
an indoor place to shoot, that has a wide range of rental handguns
as well. It is one of the places I first got started a few months ago.
Of course they are closest to LAX (airport) by the coast so it's a 30 min drive.
http://www.laxrange.com/
There is also The Firing Line which has a location in Burbank. Though I am
not as familiar with them, I do believe they have a smaller selection of handguns to rent and their rental rates may be higher.
http://www.firingline.net/
The next link is where I bought my first gun. They are a sporting goods
chain and have many locations throughout the LA area, including an outlet
in Pasadena which would be the closest to you.
http://www.turners.com/turners/stores.php
One of the best places to go shooting once you have your gun is at
the Angeles Range above Lake View Terrace. I like shooting outdoors
more than indoors for a number of reasons including noise.
http://www.angelesranges.com/
I would recommend that you go to LAX (with someone who can
guide you) and try out a number of handguns. To determine which guns,
the people here will help advise you and you can also use the search feature of the forum and find out a lot about the various choices out there. That is what I did, and it worked, I'm still here!
Have fun and stay safe.
cheers, ab