It's good in season 1 too, it's just more consistently good in season 2. Although the story does advance over time, most episodes are standalone, which you could interpret as filler.
In season 1 here are the most important episodes as far as the main arc goes:
1, 6, 8-11 and 13
That's just over half the season. If that is too much for you to watch read these descriptions and watch the ones that seem most important to you. But you may miss something important.
Episode 1 explains why Star is sent to earth.
Episode 6 is about Star going through Mewberty, which may be relevant later, and also has the first sign of Star being attracted to Marco.
Episode 8 is the Blood Moon Ball, definitely important to the show's plot.
Episode 9 introduces Father Time who has appeared in season 3 and may appear again. Also it goes into Marco's crush on Jackie
Episode 10 has Miss Heinous who is due to appear in the second season, may be important.
Episode 11 is Mewnipendence Day which goes into the lore of humans v. monsters a bit and shows that it isn't so black and white.
Episode 13 is the finale, big stuff happens there.