Yes, the username and password you assign at the welcome screen after a successful install is the "admin" account. Also to answer the second question, no you will not have to log in as "admin" to install programs. You will however be prompted with a login dialog whenever you place an app in the Applications folder. All you have to do is insert the "admin" username and password for authentication.
Running a limited/standard account is best practice. I do this to all my machines and it's just a precaution to whenever a virus or trojan becomes wild. It's just a matter of time before OS X is targeted more. This isn't anything like antivirus, but it does stop apps from running unless you insert your "admin" credentials. A few years ago (2006?), someone started to spread a file that supposedly contained exclusive Leopard screenshots. Turned out it was some sort of worm known as OSX.Leap.A. When people would open the file and double-click the pictures, the admin dialog would pop up. Why would you need admin privileges to see a picture? Anyway, long story short ... non-admin users were more protected. Within admin accounts, the worm was able to run without the user knowing what just happened.
Also might want to check this old thread out. Someone was asking about viruses/spyware and I gave out some helpful tips for staying secure. Also has some good links at the end that you may want to check out. All this is for OS X 10.4 Tiger, but most of it still applies to OS X 10.5 Leopard.
For the lazy, here are the links I was talking about.
Corsaire's Securing Mac OS X 10.4 Tiger (.PDF) By Stephen de Vries.
Here the easier one to read from Princeton.
Just to let you know, I am not a security expert. Just a poor medical student wanting to stay secure.