To answer Flipcollar's questions before I myself am called out, and to actually give some programming advice as someone who is barely getting to an above average point:
Started benching 70 lbs for 3 half reps at 15ish. Senior year of high school pressed 285 with a magnificent bounce. Have now (age 22) benched 365 with a slightly quick press command in "competition" (unsanctioned meet) at a bodyweight of 182 lbs and 6 ft tall.
Dips are your friend. The more dips I do, especially heavier weight, lower rep sets, the better my bench feels. Rep schemes like 5x5, 8x4, and 6x6 are my favorite.
Lats and upper back are important. With longish arms, I have found (for me, anyway) that a wide bench grip allows for more weight to be moved. However, I find the eccentric portion of the bench can feel really awkward. The more consistent I am with back work (weighted pull-ups, db rows, face pulls, etc.) the more controlled my lowering becomes. I feel better lowering rather quickly instead of slow and methodically, and having a capable back helps control a quick descent.
Overhead pressing doesn't seem to have much carry over. Overhead pressing work makes my elbows hurt and my hands numb; and the pain plus the accumulated fatigue from extra movements takes away from the frequency I can bench. Lots of strict lateral raises, incline pressing, and mounds of rear delt work make up my shoulder training, and I feel much more "healthy" in my shoulders and arms since abandoning strict overhead barbell pressing.
Also, try to bench twice a week. I like a heavier low volume day with a lighter high volume day. Also, I focus on chest for one day of accessories and shoulders/triceps for accessories on the other. I rarely bench for sets higher than 6 reps (again, seems to aggravate my shoulders) but I push the volume with the accessories that are comfortable.
Here is an example training schedule (although since I have no idea your training age or weakpoints, we can talk tweaks if you come back to the thread). I'll use the bench numbers you gave as a rough estimate for volume and training weights.
Bench Day 1:
3-5 sets of 6-15 reps with whatever load makes them challenging.
DB Bench or Flies or any other chest focused movement for 5 sets of 10-20 reps
Bench Day Two:
5-8 doubles with 155-165 lbs
Incline BB or DB Press
4-6 sets of 8-15 reps
Close Grip BB Bench or Neutral Grip DB Press
3-5 sets of 10-20 reps
DB Laterals and Face Pulls till you're shoulders are tired.