There's basically three "sets" of games in the series. 1 and 2 are really old, have very little graphics, and (mostly) require the player to draw his or her own maps. They also have separate, text-based screens for turn-based combat. They are probably the hardest to get into because they're so old, but they're actually very good if you can get into them.
Games 3-5 still feature turn-based grid-based movement but combat now happens right on the map, without a separate screen. They have improved graphics that are colorful and still look pretty good, but are obviously dated. Many consider these games to be the best in the series (I'm partial to 4-5, but I haven't played past 6; many players think 7 is best).
Games 6-8 (and 9 I guess) are the most modern, with a fully 3D world that can be explored in real-time. Combat can be toggled between real-time and turn-based. Many consider these to be the best, especially 7.
There's not too much connecting the games to one another, but there are some cool details for those who have played in order, which are a nice bonus. But you could conceivably start with any of the games. So it comes down to what you're looking for. If a really old-school (made in 1986!) game that makes you draw your own maps (or look them up online) doesn't scare you, by all means start with the first game, but if it's too old for you then try number 3. If that's still too dated, maybe jump to 6.