That's a bunch of questions! Let's see -
What is a good backup app for my cell phone? -
Several of the folks here use Astro File Manager to back up their apps. There are others as well.And....do backup apps backup everything on your phone so that when you upgrade etc. you will have all the information ready to sync to your new phone? -
No... However there are several groups of items to backup and different apps available to do the job. Most backup apps copy your "apps" although there are some that will copy photos, music, contacts. I have no experience with any of the all-in-one apps but I believe they are out there.
If you sync your contacts with your G-mail account they will be backed up continuously, I highly recommend it.What are the pros and cons in a backup app vs. backing up your cell phone to your computer? -
Copying the contents of your SD card to your computer is a very good way to back up apps (especially if you are using Astro's app backup as well), photos, ringtones, and music. This is the way I do it.Many questions!
Yes! 
thanks any information you can share.
You are welcome! 