Offering tips for caring for an entire type class is a tricky subject, anonymous, because members of a type can vary wildly in terms of physiology. For example, any tip I have regarding caring for a butterfree absolutely cannot apply to charizard, mantine, or minior, and the kinds of concerns one may have for training a sigilyph or scyther aren’t the same as the concerns one may have for training a hoppip. Care comes to down to species, not to type, and that goes especially for a type affiliation that’s as diverse as flying is.
However, I can at least comment on which would make good partners. In truth, all of them would, but I presume you mean for someone who’s new to raising flying-types. In that case, the flying type consists of not only one starter (rowlet) but also many pokémon commonly found among “beginner” routes, such as pidgey, hoothoot, taillow, and so forth. All of these adapt well to human interaction, and they’re often loyal or otherwise receptive to instruction, making them easiest to train. For those interested in training for tournaments and the like, skarmory, hawlucha, and starly (or, more accurately, staraptor) tend to be popular choices, but zubat (or, more accurately, crobat) and wingull/pelipper are both fairly common choices. Finally, if you don’t mind raising a non-flying-type for a bit, there’s a lot that can be said about gyarados, salamence, dragonite, and charizard. (Yes, contrary to popular belief, training a magikarp is worthwhile. In my personal opinion, even if magikarp didn’t evolve into gyarados, they’re fascinating pokémon worthy of being trained, but that’s neither here nor there.)
So in short, it would perhaps be dependent on what you wish to do, anonymous, but there are plenty of good choices for flying-type partners … and plenty of different ways one could care for them.
The Pokédex According to Bill 