Well if you are into customizing, rooting, and power. I would say the Note 2, SGS3, Nexus 4. The reason I really hesitate to add in the N4 is the lack of storage space on there. I do not leave a whole lot of room for games. It will have good developer support so customizing will be there.
The other two will be great in that area too, the N2 is a bit behind because it is newer, but the support and ROMs will be there. The N2 is the more powerful of the two devices, again it is newer, but the SGS3 is no slouch at all. It is 6 months old and still one of the top phones out there without a doubt.
The route I went was the SGS3 and put a version of CM10 or AOKP on it. It gives me all the advantages of stock (the Nexus) without any of the crippling limits the N4 has. 32GB storage, SDcard slot, good battery life, removable battery if I need to swap them out...the list goes on.
Other good phones out there are the DNA (great screen, no storage or removable battery, not easily customizable), the Razr line (verizon only, totally locked bootloader), the optimus G (bad camera).
I think you should pick a company first, then see what they have to offer. As far as that goes, I am really digging Sprint. I have good LTE coverage around me, the price is better than Verizon and they seem very helpful over the phone when i was shopping around. The only limit on data is that there is a 300MB data cap when you are roaming. I don't see that as a problem.
Use sensorly.com and see what your coverage is like.