Make you life super easy and just buy a NodeMCU ESP8266 board. No need for an Arduino UNO or MEGA at all. It has all of the IO you’ll need for a simple project.
If you’re going to use WiFi, the ESP8266 is by far the most stable WiFi platform that I have used. Just be sure to use the v2.3 ESP8266 Board support package as the new v2.4/2.4.1 version has a big memory leak in it. This is not in the ST_Anything code.
Trying to get an UNO or MEGA to work with the ESP01 is not a good noob project. The UNO only has 2KB of RAM, so it is difficult to get the code small enough. Also, you really need the MEGA’s extra HW UARTs to communicate to the ESP01 due to speed requirements. Again - DON"T DO IT! The ESP01 as a WiFi dongle has NEVER worked very well in my testing.
BTW - this thread is pretty old so you may want to keep an eye on the newer thread at