School Club with $1000 budget

Hello! I am the leader of my school’s science club. For this year’s project, we decided to build a wheeled robot! But, we do no have any knowledge about robots though I myself am very proficient in programming. We would like to know what products we should use for our robot. Only three of our ten members are very tech savy. Thus, we prefer if we could build our own base and not use any kits so at least the other members can do something. So, below is what we know and if you guys could help suggest what parts we should do and what “How-to” videos or instructions we should use (it can be pretty advanced instructions since I can understand it). Here is what we know so far:

Budget: ~$1000 (we can push a bit more if needed)
Size: 2ft wide x 3 ft long (base made out of wood?)

Must Features:

]atleast 4x4 AWD (up to 6x6 AWD)/:m]
]Arduino Controlled (other reccomendations are welcome!)/:m]
]Airsoft gun (360deg aim)/:m]
]live camera feed/:m]
]speakers (play music via USB or via WiFi)/:m]
]Turbo (super speed), though how it would work, I don’t know, maybe temp electrical output boost?/:m]

Optional Features:

]Water gun/:m]
]screen (display message)/:m]
]I’m open to suggestions! (looking for something cool/fun/explosion-y?)/:m]

Again, I am new to robotics, so if you have any suggestions or recommendations for me, let me know!

First things first, take a look at the How to Make a Robot Grand Tutorial. Follow the steps to get a few designs in mind. Next, use the Drive Motor Sizing Tool to get an idea of the motors you will need. Carrying around water for a water gun adds a lot of weight which in turn makes the robot more expensive.
The main expenses will be:

]4x drive motors/:m]
]1x high power dual motor controller/:m]
]5 channel remote control (two for steering, two for pan/tilt and 1 for trigger)/:m]
]Pan/tilt able to move a somewhat heavier device (airsoft gun)/:m]

If you plan to make it remotely controlled, there’s not a lot of wiring to do since everything can be plugged into the receiver.

One of the difficulties is finding a motor + hub + wheel combination. Once you have that, you can start designing the frame.