Remember that the first boot after installing a new ROM takes much longer time than an usual boot.
Sometimes it takes up to 10 minutes (maximum), so be patient.
As for myself, I have to flash a custom ROM frequently but I always prefer a custom ROM that keeps me near to the stock Jelly Bean 4.1.2 firmware of my Galaxy S3 (with all its bloatwares) but gives me a better battery-life, smoother user UI and a few other tweaks and mods.
Quite recently, o example, I had been using the Paranoid Android ROM 3.0 and I must admit it was a very lovely experience for a week.
The Galaxy S3 is an immensely popular Android phone and it is by far the most-selling phone from Samsung and therefore it has been a darling among Android developers.
This has resulted in hundreds of custom ROMs and mods, so much that it might confuse a person who is planning to switch to a good ROM on his Galaxy S3.
The credit goes to the respective developers for working hard for us.
We would like to clarify the we are not the developers of any of the ROMs listed here.
It is based on AOSP 4.2.2 and also supports themes made for Cyanogen Mod 10.1.
The ROM is almost bugless but the PA Team will have to focus on improving the battery performance a little.
The PA ROM now comes with another innovative feature called Halo Notifications.
Below is a video overview: I have written a detailed article that reveals all the aspect of this new avatar of the Paranoid Android ROM.