There are essentially four different basic types of harmonica.
Diatonic
Chromatic
Tremolo (and octave)
Orchestral
The 10-hole diatonic is what you usually hear as 'blues harp' and is the most common in the US. There are other hole configurations for the diatonic too, from 4-20+, but the 10-hole such as the Hohner Marine Band, Special 20, Blues Harp, etc... are what you'll see most tutorials and learning materials intended for. C is usually the best key to start off with though some people prefer the deeper sound of a low G.
The other three types aren't really for doing blues and bending stuff with. The chromatic and tremolo are best suited to folk music and because you'd be playing more melody type stuff than improvising blues, it can be beneficial to have 20+ on those. These are what you usually see as the longer harmonicas when you find one in a shop.
The orchestrals are usually long too (sometimes very long) and rather expensive. They are mostly for playing in harmonica orchestras/ensembles and aren't so great for the blues at all. Check Youtube for Harmonicats for a good example. A group of them sounds like a huge accordion. http://www.youtube.com/watch?v=0OfJENYhsrw&feature=related (a chromatic, chord, and bass)
If you're a beginner and want to play the blues then start out with a really good quality ($30+ range) 10-hole diatonic in C. A lot of players are pretty fond of the Hohner models mentioned above and Lee Oskar models. You might want to avoid the sub-$10 models unless you're just wanting something to play around with a little.
If you're a beginner and want to play folk tunes and melodic stuff then look at the Hohner Echo Celeste or the Suzuki 2-timer in C as a good starting point. Both are 20+ double holes and relatively inexpensive.
Chromatics (easily identifiable by the button on the side) aren't usually a good place for a beginner to start but if you have some dedication to a practice schedule it can be done. They aren't inexpensive and aren't as care and maintenance forgiving as a diatonic or tremolo.
http://www.youtube.com/watch?v=gX0aM_ui3cY is a nice video from the folks at Suzuki demonstrating the different types and some of their models.
[note: most of mine are Hohner but I also own a Suzuki SU21H [ http://www.youtube.com/watch?v=GrL1Pg-Kptk&feature=mfu_in_order&list=UL ] I play almost exclusively tremolo harps in folk style.]