It's hard to know for sure if Nixon would have been forceably removed from office. Even Presidents Andrew Johnson and Bill Clinton were impeached, yet not removed from office. That being said, public opinion was largely against Nixon, so it's possible the country would have gone through a difficult time and he might have been removed from office at some point. He did the right thing by stepping down before the country had to go through that type of turmoil.
There had been instances of impeachment before Nixon, but Nixon himself was never actually impeached, contrary to popular belief. Nixon would, however, have been removed from office, as can be seen both in the opinion and stance of Congress at the time and in hindsight, making him the first in US history.
Yes, Richard Nixon should have been the first U.S. President to be removed from office if he had not resigned, because he did a terrible thing that violated the public trust. What Nixon was a part of amount to a felony. He rightfully should not have represented the public after that. Clinton should have been removed from office, too.
Had Richard Nixon not resigned in 1974 he most likely would have been impeached and removed from office. The evidence was clear at that point that Nixon was in fact guilty of multiple offenses and his impeachment was practically guaranteed. This would have been followed almost certainly with his removal from office. He therefore resigned to avoid such a fate.
I believe Richard Nixon made mistakes in the White House that would have lead to him being removed from the office had he not resigned. With that being said, I think he would have gotten away with his acts, in today's world, which is not justifiable, but a sad fact.