This is a difficult question to answer, especially since you haven't given a specific size. W/o a lift a bigger tire will rub. Even with a lift, you could still run into rubbing with bigger tires. If you are stock right now, I would say a 265/70r17 is the safest choice. And there are tons of used sets in this size for sale. There might be slight rubbing but nothing that you have to worry about.
Finally, I'd say the best attitude toward bigger tires is whatever you do, expect it to rub and for you to do some fitting. I'm doing the same thing you are too! I ran 265/70's on stock and then 285/70's with a lift and it rubbed, however no BMC needed. Hope this helped.