Samson (aka Zoom) really makes some good recorders at excellent prices.
I have the H2 and the H4n.
I made some side by side recordings. I found the H4n to have a little more detail. Since the microphone elements are significantly larger, this is probably the explanation. The Zoom H1 has the same microphones as the H4.
That said, the H2 makes great recordings. I expect the H2n would be even better and some of the features are really nice, like the analog gain control.
The H16 is really a different animal. It's a portable mixer with built in mics.
The H16 would be good at home, most particularly if you want to do multi track recording. If you just want to do recordings of solo whistle it is a bit overkill and it might not make as good recordings as the less expensive recorders (because you can't add all those hardware sliders for free).
If you want to be able to take the recorder with you to workshops, lessons, sessions, or whatever, then the H16 will be less convenient.
If you want to make the highest quality recordings possible, then a standalone audio interface and a decent microphone will beat a handheld recorder. The H4n has 4-track recording and the ability to plug in external phantom powered condenser microphones. If you don't need these abilities, then the H1 will probably make just as good recordings for less money, and it is more portable as well.
I have a stereo pair of condenser mics with a TASCAM us-800 that I use for recording practice. I leave the mics set up and cover them when not in use. I got the us-800 because in addition to being able to plug my mics into my computer, I will be able to transfer many hours of minidisc recordings at top quality. My wife always uses the H4n. She is convinced it sounds much better than the H2, but I am not as sure about that. One drawback of either of those is you need to listen back on headphones if you want to hear detail. One advantage of the H4n is the built in speaker. It's not great, but it works well enough to hear what you're doing.