Relative to the "norms" of GA aircraft (like a C 172) , 125 knts for low fuel burn, and "not too much" is not going to happen, and no icy conditions whatever. You'll have to consider if you want certified vs non certified, though if you seriously intend to carry 4 people, there are few non certified choices.
A 550 NM range will be a stretch for most lower cost 4 place aircraft, while carrying 4 people, and really, 4 people in a 4 place aircraft traveling a more realistic 100 knts will not want to be in the air for 5.5 hours at a time anyway. Thousands of pilots and owners have been quite happy with the economy and capability of C 172/182/Cherokee for many decades, as you continue your training, consider the real world uses you would put the plane to, and then put the lesser capability you commonly need, if you really have to, you might rent bigger or faster. Search this forum, you'll find lots of discussion on 4 place aircraft choice...