Custom guitar - practically sky is the limit when you build one. problem is matching the wood for the neck and body (so many combinations for different "sounds") custom guitars are generally for people with sufficient knowledge regarding hardware,type of wood, pickups, etc. (just to make sure the person building you your dream guitar is not blowing smoke and trying to BS you for more cash) People tend to forget to research on the tonal property of the wood they will use before they actually have it built. I personally know this because I sold mine. I HATED IT. If you guys decide to go this route make sure to do your research. you dont want to spend a sh! tload of cash just to be disappointed with the final outcome. Go to your nearest guitar store and try out guitars with different wood (alder,basswood,mahogany etc)
Bnew guitar - i tried 5 american standard strats all the same except color. they all sounded different! i used the same amp same settings. my advice is try out different guitars of the same model. I'm sure anyone can tell the difference given that you play each guitar of the same model for a certain amount of time. or you can compare them side by side. whatever floats your boat.
2nd hand - In my opinion 2nd hand guitars have more soul to their sound. specially gibsons and fenders. you can really hear the difference. I may sound redundant but try out the guitar. I find it easier to connect to used old guitars.
To sum all this up in a nutshell research and try out the actual guitar. don't get blinded by brand names or signature guitars! If you really want a unique looking sounding 1 of a kind guitar then go custom!