Nexus 4 apps

Hello!

I bought myself a Nexus 4 about five days back. I'm absolutely enthralled by its overall performance and the speed. Feels great to have a phone that doesn't show even the slightest indications of a lag (I used a Samsung Galaxy 3 for 2 long years by the way).

Since I'm new to this high-end smartphone league, I'd be grateful if you could give me a concise list of must-have applications. I use my phone primarily to text, tweet, browse, mark deadlines and lists and play games once in a while. (I don't use my phone for listening to music AT ALL). A brief list would do.

Going by my usage for the past five days, I'm not all that impressed by the battery life. It somehow seems to drain pretty quickly though I have installed minimal apps as of now. I also read somewhere that the battery life improves after the first few days. Is that true?

I did buy a case for the phone but absolutely loathed it. The phone without the case is a delight to handle. The form and design are just beautiful.

Thanks in advance!