Might want to go to the Powerlifting/strongman site for some serious examples and advice for benching programs. If your into BB'ing but just want to boost the bench poundage, up than an overload system may be best for you. Sounds like a RAW benching event, without any lifting shirt/suit, that draws your interest.
The basic three pin position in a power rack almost always insures a rapid increase in weight hoisted. Start from the upper lock position of 3 to 4 inches and work down from there. Can also do regular sets of 3's X5 or 6 sets. Have to get use to working with weights heavier than normal on a regular bases. Chains and bands are well advised, but can take some time to get use to. And also doing them the correct way. The month of May will be approaching pretty fast, so time may be a factor in learning to use either correctly. That would also include speed and timing work, which can take months to perfect. If you had two or three months, than your training would be geared for more advanced training methods.
Don't want to go to complete failure in any benching exercise, PL's do not. Just train hard and steady twice a week, testing a max rep about every 2 weeks. You will know when your getting stronger anyway by the weight used in regular benching workouts. Some auxiliary exercises in a bench program would be the PBN (Press Behind the Neck) and dips. Also tricep extensions, usually preformed with a DB, insuring both arms develop equal strength.
I'm not big on supplements, just good eating habits of quality fats/oils, carbs & protein (the usual suspects). The only one I might suggest is Creatine Monohydrate with Tauine. The one's with the dextrose/beet juice are the more easier absorbed and used in the blood stream. Most of the athletes I've know, who used this stuff for strength and size, have seen results in fairly fast order. Good Luck.