Battle Network is fun as hell, but I would
not start with the first one. I'd also say to skip 4 if you like fun.
The games, in order from best to worst are 3/6, 2/5, 1, 4
1 isn't
bad but it hadn't come into its own as a series quite yet.
Anyway, brief overview of Battle Network games: They're basically an AU where Light's networking research got chosen over Wily's robotics. Everyone lives in a futuristic society where everything, including ovens, dishwashers, and chalkboards, is online. To guide people through this they have net navis, basically little AI programs that reside in everyone's PErsonal Terminal (or PET), which is essentially a smartphone.
The series follows Lan and his navi Megaman, Megaman being Lan's twin who died shortly after they were born.
Gameplay is incredibly different from the regular series.
Really just watch this video of a boss battle from 3 to see how. You wander around an overworld, and in internet areas you have random battles that play out like that one.
They're not really hard (except for a few notable bullshit bosses and stages) until you hit the postgame on a lot of them, and they're a lot of fun.
Four is horrible in a myriad of ways and I would only play it if you KNOW you like the series.
A word of warning: Computers are magic and there is exactly one person in the series with common fucking sense.