The three “standard servo motors” – presumably standard-size hobby RC servos – will be the main load on your power supply, unless your LEDs are high-power devices. Pololu.com's electrical characteristics of servos... web page has some guidelines you probably should read. Some excerpts:
... A standard servo will have a stall current around one amp, a micro servo will need a few hundred milliamps, and a giant servo can draw ten amps or more. ... quiescent currents are tricker to estimate ... typically, the current should be in the few dozen to one or two hundred milliamp range
For your three servos, a 5V 2A power supply is reasonable, supposing you never stall more than one servo at once and that stall times are brief (a few seconds at most). If you were to stall all three servos at the same time on a 2A PS, and the Uno were powered by the same supply, it probably would reset or otherwise misbehave.
Figure 35 to 50 mA for the Uno, and perhaps 50 mA for the ArduCam Mini 2MP camera (125 mW at 3V, IIUC), and 15 to 25 mA per LED. Note, for indicator LEDs (vs illumination) many high brightness LEDs work ok at sub-milliamp currents; for example, on some of my Arduino nano boards I've replaced the PWR indicator's 1KΩ dropping resistor with 20KΩ and it's adequately bright.
In brief, allow two to three amps for the servos and perhaps a fourth of an amp for the rest.
The Arduino will draw only the current it needs, as long as it's powered via USB or its Vin pin or DC socket. Several Arduino models (eg Uno, Mega2560, Nano) have a FET or diode automatic power-selection network, typically allowing them to be powered by USB at the same time as by Vin pin or DC socket.
If you wish to connect a 5V PS to an Arduino's +5V line (which can be done), first review the “gotcha's” at 10 ways to destroy an arduino at rugged-circuits.com.
For a 12V adapter, hook into the Vin pin or DC socket. On an Uno, there's a diode after the DC socket and in this case using the socket is preferable to using Vin.
With 12V into the Uno's +5V regulator (typically a NCP1117ST50T3G), you probably won't draw more than 0.3–0.5 A from the +5V line without overheating the regulator. A 9V supply, dropping 3V less across the regulator, dissipates 1.5 W less power in it at 0.5 A than does a 12V supply, with consequently less heating.
An Uno page at arduino.cc says:
The board can operate on an external supply from 6 to 20 volts. If supplied with less than 7V, however, the 5V pin may supply less than five volts and the board may become unstable. If using more than 12V, the voltage regulator may overheat and damage the board. The recommended range is 7 to 12 volts.
Note that hooking a 5V PS to the +5V bypasses the regulator entirely. The earlier link (10 ways...) recommends against this in certain cases. The Uno page at arduino.cc advises against it:
5V. This pin outputs a regulated 5V from the regulator on the board. The board can be supplied with power either from the DC power jack (7 - 12V), the USB connector (5V), or the VIN pin of the board (7-12V). Supplying voltage via the 5V or 3.3V pins bypasses the regulator, and can damage your board. We don't advise it.
Power Arduino and low-current devices via USB or via a 9V 3-5 W adapter; use a higher-current, eg 2A or 10 W, 5V adapter for servos.
With a 5 A or 60 W, 12V adapter, connect +12 to Vin or DC socket; also attach one or more inexpensive adjustable 2-amp LM2596-based buck regulators like 1, 2, or 3 to the +12, dial the outputs in to +5, and use them to power the servos, with the Arduino ground common with the regulator grounds.