If you want vanilla android, your best bet is Cyanogenmod
or another AOSP ROM, such as Slim bean
, which come in Android version 4.1.2 [Jelly Bean] and 4.2.1 [Jelly Bean MR1]. These ROMs are very similar to the one you would find on a Galaxy Nexus or Nexus 4, but with lots of added features.
Cyanogenmod is currently on version 10.1, which is Android version 4.2.1. You can find download links here - CyanogenMod Downloads
. I haven't tried 10.1 yet, but I must say CM10 was extremely buggy and there were a lot of things broken, and there can only be more bugs in 10.1.
I've heard Slim bean is quite good, but again it will have a lot of bugs too, as the developers do not have the proper sources to make certain things work (such as the hardware composer and the camera.)
From what I've read, I need a modem, kernel and ROM - is this correct?
Mostly you need the ROM, as it will contain a modem and a kernel with it, however you can flash different ones if you would prefer. Siyah kernel is a very good one, but will only work on CM10 (please be careful if you decide to flash another kernel and check if it's compatible with your ROM
On my HTC Desire HD, I couldn't wait to get vanilla android on it because I didn't like Sense at all, but with my S3 I think they have done a great job on Touchwiz, and a lot of things they have added have been useful to me. But I can understand why people want AOSP