What are the best apps for saving battery life and memory?
As far as battery life, there are a few apps in the market that allow a great deal of customization for CPU speed, screen brightness etc but I think you have to be rooted to use them. Honestly, the best way to manage battery life is to: Get the extended battery from Verizon, turn down your brightness to as low a level as you can tolerate, don't have GPS, WiFI and bluetooth turned on unless you are actively using them, make sure your phone is in CDMA mode not Global, if you have downloaded a task manager get rid of it, live wallpaper is pretty but it uses alot of battery, if you have apps (weather, email, facebook etc) that update at certain intervals, either update manually or set the update frequency to as long as you can tolerate. Normally, your screen uses more battery than any other function...so the less time your screen is on the longer your batter will last. If you follow these suggestions you will see a significant increase in time required between charges.
Memory: Unless you root your phone, memory management is more about you managing what you put on your phone. It's great to have all kinds of apps in your apps drawer. All those icons look pretty, but all those apps take up memory, even if you can move some of them to your SD card. The only way to get rid of unused/unwanted apps that came on your phone is to be rooted, and rooting is a whole different topic, but one you should look into whether you decide to root or not...good idea to understand what people are talking about in these forums when they say something about "root". There is little you can do, without root, to manage memory aside from installing only apps that you will use frequently. Having an app that installed that you never use only eats up storage space. Android does a good job of managing it's available resources...it will turn apps on and off as it needs them or doesn't need them...there is little you can do to control that...even with root.
Bottom line...get extended battery, turn off or turn down functions that eat battery (screen, updates, GPS, WiFi, bluetooth etc), manage what you put on your phone to those apps that you frequently use and let the Android system manage its resources. Get rid of any downloaded task manager...they usually use more battery that they are worth and often cause more problems than they are worth.
Forgot to mention...there are a number of pretty good cache cleaners in the market (free). Like a PC, it never hurts to clean out the cache every day or so.