I was leaking a lot for first couple of weeks, and was paranoid about it. Depends briefs are the best, but if you're going through a lot, any cheaper brand will work. At night, I added a pad that I could take out without changing the Depends.
After the leaking slowed down, I used a pad during the day in my underwear, and that gradually went to shields (Tena) and nothing now unless I am going to be very active. I prefer boxer-briefs. They are tighter to your body and legs than regular boxers, and I found the pads less likely to slip. My favorite brand is the Duluth Trading Post "Bullpen" boxer briefs. They have a pocket in front (for your junk) that holds apart pad or shield right in place.

Agreeing that those protective absorbent mats to have on your bed is a good idea. Mattresses are expensive.