The stock boxed Phantom from DJI has a full set of extra props (total of 8). If you don't hit anything, they don't break and wear out. I still have the original 4 on my P3P from January.
The boxed Phantom comes with a single battery. Its good for 15-20min of flight time and takes >45m to charge typically. So, any package that offers extra batteries is what I would go for. Three (3) total (1 from bird, 2 extras) is a good starting place. About 5 are needed for infinite flight (ie charging and recharging). You don't need 5 to start. Two or three are a good base.
You will need some sort of "smart" device such as a smart phone or tablet. Android or iOS, both work nearly identical and just as well. Be sure to check Mike's site
www.PhantomHelp.com for a list of recommended and compatible devices. If you are prone to Android devices, I particularly like the nVidia Shield K1 tablet. Its a rock solid performer and its speed/power are top notch. I don't do apple so I can't make any recommendations for an iOS device, but Mike's site has many listed.
An extra uSD card is also a nice to have extra to begin with. The Phantom comes with a 16g card. Its sufficient. I would recommend you pick up at least an extra 32g uSD card (SanDisk Extreme UH1 recommended). I typically go out with 3 32g cards, one for each battery. I change battery, I change card. No, not because its full, but because if I crash and the card is damage or lost entirely, I am not out all the files from the entire outing, just the ones I took during that single flight. It also provides a field backup in case one goes bad. If you are out with a single card and it fails, game over. If you have a second or third card, you can still go on and fly and get photos/video.
Anything else is just gravy on the taters.
3rd Party apps like Litchi (which I personally use 100% of the time) and Autopilot are also something you may wish to investigate but are not required as the DJI GO app may be enough for you.
Prop guards are another commonly suggested accessory. I have never used them. But I also don't mow grass nor run into walls and trees with my Phantom. There is a certain logic in having them while you are learning and I can see them being useful if you do a lot of flying in closed spaces or indoors.
Stuff like ND filters are a good to have, but not required. You can get along without them most of the time. You don't really need them to start out but as your photography needs expand they probably should be one of your first new acquisitions.
I argue that supposed gimbal protectors are unnecessary and actually could cause more damage so I would stay away from them. Others tout their protection. I wouldn't put them on mine. You are welcome to put them on yours. Do your research and think it through first would be my suggestion.
There is no true NEED for a case. But they do make it easier to organize and carry your Phantom. There are generally two tacks on these. Hard and soft cases. Hard cases offer the best protection. They stack easily and you can put other stuff on top without worry. If large enough, they provide a clean elevated surface to take off from if there are high grass/weeds or dirt/sand in the takeoff area. They are also heavier and way less carryable than soft cases and in most cases cost more. Soft bags are squishy and offer less impact protection but they typically come in the form of a backpack which makes them very comfortable to pack your phantom into remote areas without drawing attention to yourself. They are generally lighter and typically cost less. If you decide on a case its worth it IMHO, to get one that allows storage with props attached. Saves time and headaches. You can always buy a plain backpack and cut and insert your own foam to make your own case if you are willing to do some DIY legwork.