Congrats! 
Yes, you should update to the latest firmware. And I advice you to watch all the videos you can (especially the tutorials from DJI) and reading the manual truly is not a bad idea. It will all take some time to fully sink in, speaking from own experience ;)
Best advice is to arm yourself with patience (unless it is inconsequential for you if you smash up your shiny new Phantom ;) ) Baby-steps. It does take an effort to learn this thing. Driving a car is easy enough - but not if you don't know how to  It is sort of the same with these flying machines.
If you haven't flown a quadcopter before, I would get a "toy" quadcopter first and learn to fly (might be too late for that now you already got your Phantom 3). I got myself a Hubsan X4 quadcopter and trained on that. The basic mechanics are the same - and since the Hubsan is more difficult to fly, you will feel quite confident flying the Phantom after mastering the Hubsan And it won't matter too much if you crash the Hubsan. It can take a beating - and it is MUCH better than crashing your expensive flying camera.
Like I said, go about it without rushing and don't take chances - or you will be likely to do something you'll regret later  Even simple things like installing new firmware can be daunting if you are not used to that sort of thing. So re-read the instructions 3 times and do what it says (Don't get too confused when it updates in 2 minutes rather than 25 as it says in the instructions).
Good luck and welcome! I bet you'll get bitten by the bug like so many others around here 
- Buy your DJI Phantom 3, DJI-gear, extra DJI Batteries, DJI Hardshell Backpacks from the DJI Store by using this link - it'll help me out 
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It is sort of the same with these flying machines.
Even simple things like installing new firmware can be daunting if you are not used to that sort of thing. So re-read the instructions 3 times and do what it says 
