C is most common because most of the tutorials out there are done on a C harp. It's useful for playing in C (not an uncommon key for folk music) and in G (crossharp).
Guitar players tend to like to play in D E and A (sharp keys) and a huge amount of music in the folk, county, bluegrass, and blues genres is found there. In crossharp you'd have A (on D), B (on E), and E (on A). You'd get D crossharp on a G harp (which is why G is a really popular key to own).
Horn players (especially jazz players) like flat keys - in good part because their instruments tend to be in either Eb or Bb. C, Bb, and F are good for playing with horn players. In crossharp you'd have C on an F harp, Bb on an Eb harp, and F on a Bb harp. C harp gives you G in crossharp which is a simple sharp key for horn players.
So that's about the key. If you're playing alone it doesn't matter at all. If you're playing with others then you need to be in the same key they are. If you're playing a lot of different music with a lot of different folks, you'd need a whole set of keys. If you write a lot of music, analyze what keys and modes you tend to write in - that's probably what your ear likes most.
Which harp you buy depends on your personal tastes and what you're going to play. 10-hole diatonics can't be beat for blues playing and for the "three chord trick" in chord vamping. A good choice there is Hohner and specifically the Marine Band, Special 20, Blues Harp (not Blues Band), Big River. etc.. The Suzuki Manji is getting some really good reviews as are the FolkMaster and BluesMaster. The Hering 1923 is a pretty sweet blues harp too. People who like them rave about the Lee Oskar harps. As diatonics go, I like my plain-old Hohner Marine Bands. They've stood the test of time and countless pros.
If you're leaning toward folk/gospel tunes but want a 10-hole richter diatonic then the Hohner Golden Melody is really popular. It's also great for playing with horns because it doesn't use just temperament - equal tempered. They just sound right on melodic lines.
If you're really wanting to play tunes and melodic stuff (jazz, classical, etc..) then a chromatic is the best way to go. The Hohner Educator 10 can be had for about $50 but the Hohner Chromonica 270 will make you happier (and a bit poorer). Chromatics use a different scale tuning system that isn't missing those notes down in the bottom but they aren't as great for vamping chords. Some great players use them in blues though. The Hohner Marine Band 364 Soloist is tuned like a chromatic but doesn't have the slide - it's great for starting chromatic on. Also much cheaper.
Then there are the tremolos and octaves. These are pretty popular everywhere except in the US. The Hohners tend to sound like a French cafe accordion, the Suzuki are less "wet". Most Hohners are richter tuned - most Asians are solo tuned. The Hohner Echo Celeste is solo tuned and is really cheap for a great tremolo. The Hohner Comet is a fantastic octave harp. Any of the high end Hohner Echo Harps and the Suzuki Su24H are great examples of the style. They're for playing melodies and tunes usually unaccompanied or with a single guitar. They are not so good for blowing the blues because it's hard to equally bend two reeds at the same time. Octaves and tremolos have a double reed for every pitch to lend them that distinctive sound.
It sounds to me though, you should probably be leaning toward the 10-hole diatonics a few paragraphs back. You can hear most of these being played just by typing the model name into YouTube. Some well played, some not.
My best harp is a very old Hohner Old Standby in G from back when that model had a wooden comb. It was CHEAP in its day - like a couple bucks. It sounds better than any $50 harp I have and I have more than a few.
Hint: If you'd like a full set now and to build slowly over time - get the Piedmont Blues set and one good 10-hole. The Piedmont Blues comes with a case that's worth about as much as the whole set costs (less than $25) and as you build your collection just take the Piedmont plastic out of the case and replace it with your good ones. If you keep a clean harp (they're plastic, you can wash them) - give the Piedmont Blues harps to young relatives as you replace them.
Happy playing and be prepared to suffer the dreaded harmonica acquisition syndrome disease - you can never own enough harmonicas.