There are a zillion (literally..) different 10 hole diatonic harp models to choose from, so how do you decide which to get? There are two basic classes of diatonic harmonica: ones that basically work okay, and ones that don't. Here's the main thing--look for harp models that come in all keys, and not just one or two (typically C, or C and G). Part of it is, as always, how much you want to spend--and price varies quite a bit. Here are some popular models.
Some people believe certain tonal characteristics are associated with different comb materials, but there is little or no objective evidence to support that belief. I have heard Big River harps made out of everything from light foam to lead to concrete to balsa wood to titanium, and any difference in tone due to the comb material is minimal at best. My advice is not to select a harmonica based on comb material with the idea that the material will have a "warm" or "mellow" or "bright" sound.
The purpose of the comb is to hold the reed plates and direct the air over the reeds. The most important characteristics are stability and geometric integrity--in other words, they need to be able to be manufactured accurately so that there are minimal air leaks between the comb and the reed plates. Plastic works fine for this. So does metal. Wood is more iffy in that there is much moisture involved in breathing through the harp, and wood can swell, crack or split. That aside, the wood comb Marine Band is the most popular harmonica out there, and often chosen for that classic Chicago Blues sound. The Marine Band has slots in its covers, which contributes to its characteristic sound. Probably many people attribute the sound to the wood rather than the design of the covers. The wood composite is a good material since it avoids the swelling problem. Plastic body harps with Marine Band reed plates and covers also exhibit the same characteristic sound--but are only available by harmonica. The Hohner Big River harp has slots in the covers similar to but smaller than those in the Marine Band.
One of the main factors that determine whether a harmonica's tone is characterized as warm or bright is the tuning used. Equal temperament tunings, such as used on Lee Oskar harps, are typically described as brighter sounding than more justified tunings such as used on most Hohner harps. For more information about tunings and temperaments than you knew could exist, see Pat Missin's "Altered States" at http://www.users.globalnet.co.uk/~patm.
I recommend starting with a plastic body harp. Wood combs can swell and be rough on the lips, and tend to be less air tight and more difficult to play than plastic or metal comb harps. Here are my top 3 recommendations, in no particular order:
Also remember, all harps can be (are!) less-than-perfect out of the box, and all will sometimes break reeds (where they go flat), especially for beginners learning bends, or more advanced players learning overblows. Many people find that Lee Oskars last longer than just about any other model, and I've personally never had one go bad. Many people prefer the sound of Hohner harmonicas, however, so you'll have to figure it out for yourself! In my opinion, the better the player the less difference there is in the sound of the model of the harp. I don't know anyone who can listen to a CD and accurately tell you what model harp is being played based on its sound.