Back about 45 degrees allows me to look ahead without straining my neck. Handlebars low in relation to my saddle means that my weight is distributed between my arms and my seat. Arms not stretched, but relaxed and slightly bent.
Try not to view the saddle on a road bike as a seat, but rather as somewhere to park your butt while riding. This is why road saddles are often narrow, hard, and with very little padding. If you want to sit on a bicycle saddle, then you need to be sitting upright, and your saddle needs to be wide, soft, and possibly with some springs under it.
In this position you will never get past riding at a leisurely pace. If this is your goal then this is fine, but if you want some serious exercise, to ride a distance at a reasonable pace, or you have aspirations to race then you need to be leaning forward for three reasons.
2.) Weight distribution
3.) Power transfer from your arms to your legs
If you are racing this is important. With hands on the drops, arms bent, in a low tuck position, the back should be horizontal making the smallest possible frontal profile. To achieve this a rider needs to be top physical condition, usually young in years and very supple.
If you are less than top physical condition, you are never going to achieve or maintain a position like this. If you are not racing, aerodynamics is less important, but a rider still needs to be leaning forward for reasons of comfort and efficiency.
Weight should be distributed between the arms and your butt resting on the saddle. If you have too much weight on the saddle your butt is going to be sore. Too much weight on the hands and you will get numbness in the fingers. It is a matter of experimenting to find what works for you.
I hate to see a rider pushing on their arms to sit upright. With the arms stretched straight, muscles in the shoulders and at the back of the neck are constantly under tension. Road shocks are going straight up the arms to pound on these muscles.
Learn to relax and lean on your arms. Arms slightly bent, they will act as shock absorbers. Constantly moving the hands from gripping the brake hoods, to resting on the bars just above the hoods, will relieve pressure on the palms of the hands. Padded gloves help also.
Power transfer from the arms to the legs:
This is probably the most important factor because it affects not only efficiency, but also comfort in avoiding back pain. Imagine rowing a boat (one with a fixed seat.); your legs and feet hold your body in place and your arms and back provide the power to the oars.
Riding a bicycle is the exact opposite; your arms and back muscles hold your body in place, while your legs and feet provide the power. The power transfer is basically the same; arms and legs need to be in opposition to each other.
Imagine rowing a boat, sitting as you would on a dining room chair, with your lower leg vertical and your arms pulling horizontally. The strain would be on your lower back and you would soon experience severe backache.
When carrying a heavy weight, you hold it close to your body. If you carried it at arms length, the strain once again, would be on your lower back.
Often, not having the desire or ability to adopt a low racing position, the remedy often chosen is to raise the handlebars to bring them close to level with the saddle. Often a rider will opt for a larger frame to achieve this end.
Once again, if your goals are riding at a leisurely pace, this is okay. However, the problem with a larger frame is, it also has a longer top tube. Arms become stretched out horizontally, while legs are thrusting downwards, the result can sometimes be lower back pain.
Raising the handlebars seems obvious, but there is another way to achieve a less severe position. Leave the handlebars low, and shorten the reach; this was the option I chose.
When I started riding again last year after a long lay off, I soon realized due to limitations of my aging body, I could no longer ride in the same position I had used previously. I actually went to a one-centimeter smaller frame, which had a top tube that was a half-centimeter shorter. I then swapped my 11cm. stem for a 9cm.
Because of the smaller frame, my handlebars are actually one centimeter lower, but my reach is 2.5 cm. (1 inch.) shorter. The result is not only a more relaxed position, but one that is efficient and has good weight distribution.
One clue that my position is right; when climbing while seated I am rock solid in the saddle. One sure sign that you are too stretched out, is when you make a maximum effort, you slide forward on the saddle as your body tries to take up its natural position closer to your hands.
Another advantage of staying low but going shorter, if your fitness level and suppleness improves, you can simply lengthen your stem to achieve a lower aerodynamic position. Leaning more forward has the effect of lengthening your body, so you can use a longer stem and still have your arms opposing your legs.
Footnote: Unless you have specific problems with your position, I suggest you stick with what you have become used to. Always go by the old, “If it ain’t broke, don’t fix it,” adage.