Need help finding right tires for new project!!!

I'm doing my homework before I get some rims. I read "31x10.50x15 on 15x8" is the biggest tire i can fit on my ride with no lift. If I wanna use the full 31 inches, and I get a set of 17 x 7 inch rims, what tire/s am i looking for????
what about if I get 18's????? I've come up empty so far searching the web, my problem is I know nothing about tires.
I found some good deals on some 17's and 18's, so if you can tell me what i'm looking for i'd appreciate it.

-Rob

 

[IZwack]

If this is for off roading, stick with the 15s, the 17s and 18s will do you no good with 31"s as there will be less sidewall. 17's work for tire sizes ~36"s and up.

 

[Tbars4]

...Here is some info on tires and wheels for you..
http://www.explorerforum.com/forums/showthread.php?t=216933

 

[OGWhiteRob216]

if I did get the 17's or 18's what is the biggest i can put on????

 

[IZwack]

It doesnt matter, only thing that matters is tire diameter. Wheel diameter doesnt say anything.

 

[OGWhiteRob216]

thats my problem i dont know a thing about tire's,
anyway I want some chrome 17's,18's, or 20's,
don't know how big of a tire I can put on them, relative to truck....
looks like i gotta do my tire sizing homework.