The important things to consider are the backspace on the rim and tire size. 15" rims are ok to use, but keep in mind not getting a tire to tall or wide. With the '67-8 'birds the fender and tub size are less forgiving for bigger and taller tires than the '69. Also, if you’re lowering the car this will limit you further.
I would stay with the same backspace as your stock rims. If you want to go to a wider tire and rim you will want a deeper offset. As to how much, other '67-8 owners will have to key in. With wider tires wider rims are needed to avoid sidewall bulge. Generally an inch wider rim is required for a wider tire.
In my case, I'm running P225/70R14 tires on stock 14x7 Rally II's on my cammer. These tires have a diameter of 26.4". My cammer isn't lowered; and I've experienced fender rubbing on steep driveway aprons and ramps with the wheels turned hard. I wouldn't put this size tire on my lowered convertible.
IMO a tire size with a 25.5" - 26" (aprox) diameter will be a safe bet being your going with a lower stance. This would calculate out to a P215/70 R14 or a P195/70R15. With a wider tire perhaps a P245/60R14 or a P215/60R15. But being a '67-8 you may have problems with wider tires in the front. If you are going to mix tire size from front to back, try to keep the tire diameter close.
I hope I haven't given you info overload. Play around with the web links and you'll get a better picture of what I tried to convey.