I usually don't like doing things like this, but I'm afraid I'm going to have to make an exception here. The first season, save Skin of Evil, isn't very good. Gene Roddenberry was still a big moderating force in the writing at this time, and it shows, as most of the characters come off as aloof, alien, and practically dripping with smugness. They love giving speeches on how much better they are than the humans of the past, how superior their non-capitalist lifestyle is, and how evil and stupid we are. I understand that Gene wanted to show *his* perfect future, but making your characters flawless and preachy does not make for interesting television. The only episodes that you'll really need to watch are the two part premeire, Datalore, and 'skin of evil', and I'm only recommending those because they have events which come up in later seasons.
Season Two isn't much better, but for different reasons; a writers strike at the time lead to much lower quality writing (hell, the season finale was a glorified season recap clip show), culminating in the simply awful 'The Outrageous Okana', but there are still plenty of episodes worth watching. If you want to skip this as well, then I'd cherry pick a few out that you should watch: A Matter of Honour (has pivotal moments for Worf's character), The Measure of a Man and Where Silence has Lease (Great all-round episodes), Q-Who (possibly the best Q story ever and the first appearance by The Borg). Season 3 was the point where the show really found its footing, and churning out quality stories.