Incoming passionate Megaman mini-essay:
Classic Megaman was truly at its best on the NES - if you're looking for the "true" Megaman experience, you'll want to start on the NES titles and skip 7 and especially 8 for now. While 7 is a good game, I'd argue that 8 isn't.
If you're a first-time player, you'll want to skip 1 without question. It's barely anything like the rest of the series - if you come to like Megaman, then I'd suggest going back to try 1.
This leaves us with 2, 3, 4, 5, and 6.
MM2 is where the series truly became Megaman, and when I fell in love with Megaman, it was because of 2. It doesn't have the best abilities, but it does have a great soundtrack, a neat cast of robot masters, and most importantly an endgame that doesn't overstay its welcome. After 2, Megaman develops a noticeable problem: the eight robot master stages are great, but once you beat them and enter the endgame, the game just drags on for too long. I'd advise having a tolerance for Megaman before delving into games like that. The point is: 2 is a great introduction to the series.
MM3 is a pretty good game that sometimes shows that it was basically a rushed beta. It has great stages, great boss fights, and introduces sliding to give you more mobility, but MM3's biggest problem is the endgame really drags. What should be the endgame is more or less half the game - and it's only half as fun as the part before it. That kind of experience could sour someone to the series, so I definitely don't recommend it as a first choice.
MM4 fixed the endgame, kept sliding, and brought in the ability to charge up your attacks. It also added some helpful secret items. I personally don't like it as much as some of the others I'm talking about, but I can't deny that MM4 is a good game and it's most certainly the easiest. The endgame isn't as huge or as boring as 3's, either, so it gets bonus points there.
MM5 is pretty bad. Just don't.
MM6 is surprisingly great. The robot master weapons you get are all really fun and most are really useful as well (so if you play 6, use the other weapons to get the most out of it), the endgame isn't too long and all of the levels in it are pretty fun. It basically takes what the series was doing before 6 and builds and improves upon it. Not everybody shares this opinion, but I love 6. I just think that maybe it's important to have a good understanding of Megaman before playing it to get the most enjoyment and appreciation out of it. But that's just me.
Bottom line: I'd pick either 2, 4, or 6. I'd say 2, but if 4 or 6 seem more appealing then by all means try it. 2 is the most famous of the series and is one of the "essential" games of all time, but you don't have to start with it if you don't want to.
