The original Mega Man may be a little rough around the edges, but it still contains the coolest weapon of the series with Guts Man's weapon. The Magnet Beam is also a neat item that's a little more clever than every other tool the series has introduced.
As for which Mega Man game is good to start with, probably not the original game. Personally I find it to be the most difficult of the series, and it's the only one of the ten which I never did beat. Mega Man 2 is fairly easy on the "Normal" setting, which is actually an easier version of the game created for its North American release. However, I believe the Mega Man Anniversary Collection has an "Easy" setting that can apply to all the games, and it kind of screws with Mega Man 2 in such a way that it isn't faithful to the original and still slightly tougher than the NES version.
For me, I'd go with Mega Man 5 or 6 as I find them a little more forgiving than the previous games. The charge shot helps a lot in reducing the difficulty, as does the slide move that the first two games lack. The robot master patterns are also more simplistic, so you don't have to deal with things like the impossible-to-dodge tornadoes that Air Man fires in Mega Man 2. Furthermore, the Wily stages in Mega Man 2 can be rather tricky if you don't know what to do, and I can see people giving up in frustration on the third stage's boss encounter after running out of the required weapon's energy.
Find an E-tank (Flash Man's stage is good for that), then use it to beat Metal Man. You'll get the Metal Blade, which wrecks everything in the game, fires in eight directions, and uses almost no weapon energy.
Metal Man's stage has two E-tanks, so there is no reason to visit another stage first.