This question/answer should give you a pretty good idea of what presidential security was like pre-Lincoln and post-Lincoln. And as Kaiser argues (if you can, I highly recommend his argument), the security detail as it changed was no more effective in Reagan's case in stopping the initial attempt on his life than McKinley in the 1901.

Insofar as what changed to lead to the increased assassination attempts, that's a little more speculative in nature. It's possible there were attempts on almost all earlier presidents, but they weren't publicized. It's also possible that plots foiled before they were carried out (as those on later presidents) were similar to plots on early presidents that simply weren't carried out due to hesitation or second thoughts.

I can't provide a more definitive answer because this is a very broad, very difficult answer. I can say, though, how presidential security changed during the 1800s (and some onwards), and say that it isn't necessarily any better or worse today at stopping attempts (besides maybe in deterring them) than it was back in the 1800s.