Best way to power my project.

I am about to start a project and I am having a problem figuring out a good way to power my project. I am thinking about using an Arduino Uno, 3 probes(temp, humidity), and a 4 channel 120v relay board (elegoo). I also might use a OLED 12854 module or just a standard 2 line lcd display.

Now the question I have is what would be the best way to power a setup like this? I have read that the board itself would not be able to power the relay board by itself most likely so I was thinking that I could let the Arduino power the probes and oled/lcd module, and then use a breadboard power supply for the 5v to the relay board?

I was thinking about just using a 12v ac/dc switching power supply to power them but a few posts on here say that that it is not a good route to go so I was wondering if a barrel splitter from a AC adapter be enough to handle both the Arduino and the second power supply?

Notes that may effect my options. Everything will be in a dustproof/waterproof enclosure. Since there will be no "fresh" air going into the enclosure I am not sure how warm the components will get.

The UNO (not the most appropriate for such a project, a Nano would be more practical) runs on 5 V as does the relay module, so you need a 5 V power supply. Simple as that.

A very practical approach is a 5 V USB "phone charger" which are available to supply 1 A or 2.1 A, which should be sufficient for your relays, display and Arduino.

If you need further advice on just how to wire the relay board, you need to give us the Web link. I could probably locate it, but I don't think it should be up to me to do so just to help with your project. Same applies to display, sensors etc.

Other than the small size is there any other difference between the Uno and Nano for this project? I just have an Uno on hand so I decided to use it instead. They both have similar specs except for one uses less memory for the bootloader than the other, and the nano has more pins.

From the components on the relay board each I/O pin would need 50ma to use the relays and all for uses a total of 200ma which is more than the Nano or Uno can handle safely according to the tech specs.

Ref links to the rest of the parts:

Arduino Uno Official

Active Buzzer

4 Channel Relay

OLED Module

Real Time Clock

So am i just over thinking this? I just don't want to hook it all up and fry the board.

Those relay modules have a transistor to drive the relay coils (each output pin can supply up to 20 mA). You just have to supply it with sufficient power at 5V. That same 5V supply can power the Arduino (connect it to the 5V pin) and the other peripherals.