You have been training 6 months.... Don't worry about drops sets, negatives, forced reps, etc... Pushups???? Come on. You should only be doing compound heavy exs.... Bench, incline and dips. Try bench and inclines with DBs if you are more comfortable that way.... Alternate if you want... People way over think this stuff. Lift big with good form to get big. When in doubt go slower not faster (especially on negatives but don't even dream about doing explosive dips!!!!). Full ROM.... Don't do half rep benches and wonder why they do nothing for you. Inclines cause of the position you can stop an inch or two above your chest but that's it... An inch or two. Keep volume low. 2-3 sets of any two (flat, incline or dips) and rotate between the three.
Don't over think it, keep form tight, wt heavy for you, ROM full, train to failure (post warm up), eat and rest. That simple.