Need Advice/Code help for Uno project

I am building a book shelf that I would like to automate a little bit of. I am trying to light the shelves themselves with LEDs, and I am trying to build a rotating mask stand in a sealed cabinet in the top for a very rare Halloween type mask. I want the mask stand to be set up on a remote control system where I can turn the light and the motor on and off via a RF transmitter, and the shelf lighting to work off of a HC-SR04 sensor, so that when you get close, the lighting turns on. IS it possible to do all of this with one Uno controller, and if so, could anyone help me out with the code?

IS it possible to do all of this with one Uno controller, and if so, could anyone help me out with the code?

Yes, definitely possible,

Most people will help you here if you show you "did your homework" and have given your project a serious try.

My advice is to start going through the tutorial section to learn about the Arduino language. There you will find lots of code including parts that will be of use for your project (you will recognize).

Advice 2: start small, understand one part before including the next part.

One thing missing in your material list is a separate power supply for the motor. Really importante.

Sorry about that, I meant to mention that I do have a dedicated power supply for both the arduino and the servo motor. I have the code from the playground for the motor, as well as for a ping sensor(not sure if it is the correct code snippet, and not 100% sure about which command does what. Still learning as I go) I am definitely doing research on what code I will need, but am unsure what is needed and what is extraneous or redundant.

I'm trying to understand how the arduino differentiates between different input sources, and how they interact with one another. I am working my way through it, and will get it figured out in due time.

Sounds like you have a good plan to me, if there are questions (also about tutorials) do not hesitate to ask here.

I found this code for the ping sensor but I really don't need the LCD portion. What I may do is try to change that part to control the brightness of the light in my mask cabinet.

/*
  This Project Uses Arduino, an Ultrasonic (HC-SR04) sensor, a servo motor
  and a LCD 16x02.
  Data from the HC-SR04 sensor is translated via ultrasonic library and displayed on the LCD (again using the LCD library).
 If the distance from target is equal or below 3 cm then the servo motor moves 180 degrees. When the distance gets greater than
3 cm then the motor moves to its starting position. 
  The circuit:
 * LCD RS pin to digital pin 2
 * LCD Enable pin to digital pin 3
 * LCD D4 pin to digital pin 4
 * LCD D5 pin to digital pin 5
 * LCD D6 pin to digital pin 6
 * LCD D7 pin to digital pin 7
 * LCD R/W pin to ground
 * 10K variable resistor:
 * ends to +5V and ground
 * wiper to LCD VO pin (pin 3)
 * Servo motor signal terminal connects to arduino digital pin 11.
 * HC-SR04 Trigger pin hooks to digital pin 12
 * HC-SR04 Echo pin to digital pin 13
 
 */

// include the library code:
#include <LiquidCrystal.h>
// include the ultrasonic library
#include "Ultrasonic.h"
// ultrasonic trig pin at digital pin 12 and echo pin at digital 13
Ultrasonic ultrasonic(12,13);
// initialize the library with the numbers of the interface pins
LiquidCrystal lcd(2, 3, 4, 5, 6, 7);

// include the servo library
#include <Servo.h>
Servo myservo;  // create servo object to control a servo
int pos = 0;  // define position as integer
int change = 0; // variable to avoid constant use of the servo

void setup() {
   myservo.attach(11);  // attaches the servo on pin 11 to the servo object
  // set up the LCD's number of columns and rows:
  lcd.begin(16, 2);
  // Print a message to the LCD.
  lcd.print("ARONIS PROJECTS!");
  lcd.setCursor(0,1); // Go to the second line
  lcd.print("****************");
  delay(3000); // wait 3 secs
   lcd.clear(); // Clear screen
   // Print standard message
      lcd.setCursor(0, 0);
      lcd.print("Distance from");
      lcd.setCursor(0,1);
      lcd.print("target=");
  
 }

void loop() {
  pos = ultrasonic.Ranging(CM); // Get the distance from sensor
 lcd.setCursor(8,1);
      lcd.print(ultrasonic.Ranging(CM));
      lcd.print("cm   ");
      delay(100);
     
     if (change == 0 && pos<= 3) {
        myservo.write(170);
        change = 1;
  }
  if (change == 1 && pos> 3) {
  myservo.write(1);
  change = 0;
  }
}