Really? The general consensus is that season 1 was TNG's worst season. That said, if you enjoyed that, just wait until you see what's to come! And I'll concur with everyone else, watching them in order is generally best. Though TNG isn't -that- serialized, so if you really wanted to skip around you wouldn't spoil yourself too much.
TNG's what made me fall in love with Star Trek, but I'll second the recommendation to watch DS9 once you're done with TNG. Well it gets slightly confusing as seasons 6-7 of TNG overlap with seasons 1-2 of DS9 and they'll occasionally cross paths and plots.