I've been getting more into taking my bike out on longer rides and am finding that I would really benefit from having a drop bar. My bike is an old Giant Rapid 2, it's almost entirely stock (I upgraded the pedals to SPD clippy ones) -- the brakes and gear switchers are integrated into the same unit which lies flat on the top of the bar. The bar is flat and has little horns at the end (taken off in the photo attached) which I am thinking of swapping out with drop bar ends.
My question is what is the best way to integrate these with the brakes that I have? Is it acceptable to use the flat brakes with drop handles rather than the trigger-style brakes I see more often? It seems like this would be a bit less safe, but I am not sure how feasible it is to change the brakes to the trigger-style ones (as in, can I keep my gear switching mechanism, buy trigger brakes and rewire just those?). I'm not looking to spend too much, maybe $50 maximum for the ends and whatnot, is it a better idea at that point to upgrade to a new drop bar or would that complicate things too much with having to buy new shifters as well? Or should I gut the whole project and save up for a better bike to begin with?
Edit: Thanks to all who replied. Believe it or not, I went to the store and spent way more than I expected I would on a new road bike and I'm pretty satisfied with it so far :).