Congrats Dave! Let your battery discharge to 1% then charge it. I have exceptional battery time with the S4. I have never experienced any lag with this device, and I've had a S3 (good device too), and a HTC Vivid. The Vivid was very laggy, so I know what it is. I don't have the animation on with the weather widget. I use SwiftKey, because I like the arrow keys. I have a Aduro case (thin) with a screen protector, and I also use ear buds as a courtesy, as I don't like hearing other people's music or conversations. I've tried all the Touchwiz stuff, some of it is cool, and some you can live without. You will love the camera after you have learned It's features. There is a lot a to learn about Android! I wouldn't root your phone until the warranty is up, and by then you will know the do's and don't about the OS and device. Lots of info on Android Central, and the people here are very knowledgeable and helpful! Enjoy the experience!
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