56 cm is probably a good place to start looking for someone who is 5'-11", but as others have said, a proper fitting is worth it. Someone who is 5'-11" and all legs might well need something larger, whereas 5'-11" and all torso might need something smaller. What feels OK to an inexperienced rider at first, might hurt after a while in the saddle. FWIW, I am 6', and have been fitted by two different shops; one says 57 cm is right for me, the other place 59 cm, with both shops fitting me at the time on Bianchis, which are measured center-to-top along the seat tube. Some bike manufacturers size their bikes center-to-center along the seat tube, and allowance must be made for this. After riding for a while, I would say that the second shop is probably closer to the mark for my ideal size, but, FWIW, I am more of an all-arms-and-legs guy, and a bit short in the torso, compared to most other six-footers, but I know other six-footers more spider-y than me. So, you can't reliably see what someone one inch taller than you is using, and subtract 2 cm, to arrive at any ideal size.

As for cost, I have not shopped budget road bikes in a very long time, looking more at mid-to-high-middle from the time I bought my first road bikes in the 1998 to 2002 time frame, paying in the low to mid-teens, so I can't be helpful there. People who have started with budget components have said a serious road rider will quickly tire of a bike with low-end components, and that mid-range is a better place to start. It is the components that tend to drive the price of most road bikes, as it is rare for a high-end gruppo to be mounted on a budget frame, and even more rare for a budget gruppo to be mounted on a high-end frame.