My BB went on an old 1980s Motobecane. We had all the right tools to take out the cups, but we just couldn't get that puppy loose. When you are removing the cup, check on the new BB to see which way it threads to avoid confusion or damage to your frame. I eventually threw the frame in the back of the car and went to a bike shop. Best $5 I've spent on biking.
I went with a cartridge BB, and I recommend it. Low maintenance and not much more expensive. Very smooth rotation and you don't have to worry about tightening the cups to get the right resistance. If your BB needs replacing, upgrade. If not, then run it into the ground and then upgrade.
I was on my third unsealed BB. They kept failing in the winter slush.