What size tire should I run with a 3" lift?

I'm looking into getting a 3" lift because I want bigger tires.
I want Nitto Terra Grapplers and I have 20" Chrome Rims.
What size Terra Grapplers should I get that are pretty wide and around 32" tall and won't rub the frame, and if there is rubbing it is minimal.

Thanks,
John

 

really not sure with the 20's but with 17's i'm running 285/70/17's

 

I'm running 18" KMC Monster wheels and 33X12.50 Toyo M/T and they rub a little.

 

I am running 265/75R16 Terra Grapplers, but on stock size 16's. I didn't want larger rims because I didn't want to get them all trail rashed.

 

Try the nitto terra grapplers size 305/50/20 that would fit. Look on 4wheelparts.com for the wheel/tire specs.

 

I thinkn I will go with 33's how much rubbing do you have and have you done any cutting?