There's a happy balance between being stretched out so much you hyperextend your lower back and having your bars so low you crook your neck ...and being so upright with your hands pulled in that you feel cramped and find riding grows uncomfortable after 10 miles or so.
That medium area, unique to us all, is what keeps us still smiling around mile 40, mile 60, etc.
Do some reading on bike fit, explain your questions to your LBS, visit another LBS (always a good idea before purchasing a mate second only to your wife), ride some different configurations of bike, play with the seat height, etc. Note that many of us 50Plussers like drop bars up near seat level. Mine feel good around 1 to 1.5 inches below the bottom of the saddle nose. When younger, I rode about 3 inches below but years and injuries (from skiing not biking) have brought those bars up.
And, quite honestly, some stretching exercises (a good idea anyway) and some miles may well make those drop bars more natural, more comfortable.
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..... "I renewed my youth, to outward appearance, by mounting a bicycle for the first time." Mark Twain, Speeches
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