It's not the weight per se, but the total volume that has the greatest effects on mass gain. Lifting a heavy weight in singles 15 times or lifting a moderate weight for 3 sets of 5 is not the same. Volume is higher on the first.
I find that a progression of 5 lbs is easier than a progression of another rep.
1 minute is good. you can rest a little longer between sets in the later sets. You can use also that as a deteminant for when you should stop and an indicator of progression as well. When you can't lift a weight after resting for one minute, you terminate the set. Recover, try again the next session up to add another set.
If you really go after this remember to take a high rep day periodically to get blood into the joint tissues. 30-40 reps for one or two sets is good for that. That'll keep you healthy.
Steve Justa had an interesting program in his book "Rock,Iron,Steel." He's a goofy bachelor nebraska farmer, but his singles program works pretty well. His advice is the more exercises you do in this manner, the fewer sets per exercise you should do, as you can burn out your CNS lifting everything at 90%. However, his program assumes you'll be performing the same exercises every day. If you can get recovery days and are doing splits, 6-10 sets is not a bad number to try and hit each session.
Sorry for the novel.