A minor, see Richard's answer (and my comment)
Which Harmonica to use
Harmonica is a diatonic instrument designed to play simple major folk tunes, however that's often not the way it's used in the modern day.
"minor harmonicas" do have some interesting applications, but they are a read herring to this question, for these applications what you want is a standard, run of the mill 10 hole diatonic harmonica.
For harmonica, a great way to play in minor keys is using "third position".
This would mean using a G harp to play in A minor.
disclaimer: the following bit is a bit of a tangent
As a general statement: anyone trying to "guess" how to play harmonicas in various keys based on "general music theory" is going to come up with some wrong answers, because it relies not just on a general knowledge of keys and chords etc. but on specific knowledge of the note layout of the harmonica, and knowledge of playing technique. For example, "theoretically speaking", you could never "guess" that a C harp is great to play in G and absolutely useless in F without knowing how harmonicas work, and are laid out.)
As an example of this, someone theoretically literate might guess that to play a major harmonica in a minor key, you want to play the relative minor. (So playing a C harp in A minor). However, while that would be a perfectly reasonable thing to guess, harmonicas don't play very well in their relative minor for a couple of reasons:
- there is no A minor chord. Best you get is the top of an Am7 (i.e. a C chord)
- the note "A" is not present in the bottom octave straight and is the most difficult bent note to get (bending the 3 down a whole step exactly, but not too far to an A flat). Even very advanced harp players find it difficult to play it in tune.
- Only one G# on the harmonica, in the middle octave (ignoring impossible for 99% of players notes)
Back to the point
Third positions is especially good on low harmonicas, because it's best in the middle and top octaves of the harmonica. Because of this, A minor sounds FANTASTIC on a G harmonica, seriously (one of personal favourites to play).
As a convention, we talk about all harmonicas as if they're a C harmonica, so that the same instructions can apply to any harmonica. So, I'm now going to talk as if you are playing a C harmonica in D minor (but if you were playing a G, it would come out in A minor).
Third position is great on low harps because holes 3 through 10 are D F A B D F A so you have 2 minor chords, and major 6th if you like (a GREAT colour tone for most latin and folk songs).
You also have a pentatonic scale requiring only 1 bend for the whole harp (add in the second and major sixth for dorian).
Only real disadvantage to 3rd position is you have to overblow to get a B flat in the middle octave. But if you can't overblow (and most can't), you don't really miss 1 measly Bb all that much. And hey, you're playing a diatonic instrument not even designed to play this music, you can't complain!
D and C whistles are both good in Am. If you're gonna get 1 get a D because it's generally the most versatile whistle, cause it's pretty much good for D G A, Em Am and Bm. So folk tunes, in a nutshell ;)
Tips for D whistle in A minor
XXO XXO gives you G# in lower octave, learn to halfhole XXX HOO for the higher octave or if XXO XXO isn't so good for your whistle.
OXX OOO gives you C, again only in the bottom octave. If it's sharp, then play 0XX X00, or again, half hole it as HOO OOO. On some whistles 0X0 000 is in tune for a C in the top octave, but not all. Generally a good rule of thumb is to half hole for slow passages where you want a pretty and in tune note, and to cross-finger if you're going to play something quick where the facility is more important than a note that's bang on.