I want to program an LCD, 4 potentiometers, 3 buttons, a photoresistor, 2 servos and a DC motor, in a fashion like so;
LCD (Shows speed of all 3 motors and time elapsed since the start, light in the photoresistor, and the current time and date. Switching through the values)
Potentiometer (4) (Control’s speed for all the motors, and one to control the contrast of the display.)
Photoresistor (Sees if the light is on and above 550 out of 1023 in the analog pin, or else the entire thing won't work)
Servos with attachments (2)
DC Motor (1)
Buttons (3) (One to stop everything, one to start everything, one to stop the rotation of one servo)
How would I go about connecting, assembling and programming these things?
Pick a part. Google "arduino 'part'". like "arduino LCD". Learn about all the different LCDs that there are and pick one to learn more about. Get the LCD. Learn how to use it. Write a small program to write stuff to it.
Then "arduino potentiometer". Learn about how to use a pot. Write a small program to use the pot and write readings to serial monitor and LCD.
Then "arduino photoresistor (LDR)" Learn how to use an LDR. Write a small program to use the LDR and write readings to serial monitor and LCD.
See where I am going with this?
When you have learned about the individual parts then you are in a position to put them all together using the code that you have for each.
When you get stuck with code, post the code that you have trouble with, tell us what the code actually does and how that differs from what you want.
Motors will need drivers (and as previously mentioned, external power supply) as no Arduino outputs can directly drive a motor. For brushed motors, if the motor does not need reverse a simple MOSFET driver will suffice. Otherwise an H-bridge driver will be required. to choose any driver the motor rated voltage and stall current must be known. Steppers and brushless motors need their own special drivers.
5 analog input pins for the 4 pots and LDR
Probably 3 pins for the DC motor driver.
2 pins for the servos.
3 pins for the buttons.
Pins 0 and 1 for Serial (debug).
That's 10 digital pins and 5 analog pins before the LCD. You don't have enough digital pins left on an UNO for a dumb LCD so you'd need to use an I2C LCD, but that uses A4 and A5 for I2C, leaving you with only 4 analog inputs when you need 5. You could switch to a Leonardo. It's the same size as the UNO but I think the I2C pins are separate from the analog input pins.
'speed of all 3 motors'??? Servos don't have a 'speed'.
If you want time and date you need a Real-Time Clock (RTC) module. Get an DS3231 and connect with I2C.
You don't mention any feedback mechanisms so you can't display the motor speeds. You can display a number related to output power but it won't be motor speed.
A breadboard won't give you an I2C port that doesn't use A4 and A5 on an UNO.
I think you could implement software I2C on pins other than A4 and A5. You would have to find libraries for your LCD and RTC that let you use software I2C.
They measured the RPM at one voltage (140 RPM at 4.5V) , possibly with no load, and display the speed you would get at other average voltage levels assuming linear response and no load. It's a rough estimate at best.
Pololu DC motor drivers. Choose an appropriate driver based on the motor power supply voltage and stall current. The rated voltage and stall current should be listed in the motor data sheet.