The short answer is: it doesn't really matter.
The longer answer is: buy the best you can afford.
Within these two answers are a whole range of possibilities, but it is sufficient to say that in this day and age, most photographic equipment is pretty good, and pretty affordable.
I myself use a Nikon D5000, which I purchased before my Regular Year at the ASCSA in 2010-11. I liked it because it has a tilting screen that, as I discovered with an earlier point and shoot model, comes in handy when photographing objects in museums that are positioned overhead or at awkward angles. Of course, by now the D5000 might be considered "out of date" or an antiquity itself. But it still fulfills my purposes, and the beauty of a good DSLR body is that you can add to it over time: I now have, in addition to the standard 18-55 and 55-200 mm lenses that came with it, added a very good 18-105 mm lens to my repertoire of camera equipment.
So, here are a few short tips for choosing equipment, etc.:
1) In general, I've found that Canon is better for point and shoot cameras, whereas the colour quality of Nikon DSLRs is far superior to that of Canons (nb: I know little about other brands). If colour is important to you, keep this in mind. Ken Rockwell (whose site I highly recommend in general) provides a good comparison of the two brands.
2) I recommend a macro lens for small objects - you can buy one, or even DIY (some tips here).
3) Additionally, a fixed focal length lens is good for all-purpose photography; as opposed to a large zoom range, "prime" lenses are the best-made lenses you can buy. Check out this article for more info.
3) If photographing objects from excavations, you'll want a copy stand or a tripod with a reversible center post. You can even build your own copy stand; I also like this discussion of copy stands for more advice (a separate post is needed for archaeological photography, I think, but this is quite detailed and helpful).
4) When photographing archaeological sites, your best bet is a cloudy day. Too much sun washes out the landscape and destroys the fine features of walls and stratigraphy. Always shoot with your back toward the sun to avoid shadows, and be sure to remove extraneous "stuff" (backpacks, sweaters, etc.) from the area within your photo frame. A measuring stick is always a good idea, but be sure to choose one that's appropriate for the area you are photographing (ie, don't use a foot-long rod in a general area shot).
5) When photographing objects through glass (such as in museums), be careful of reflections! You'll often need to move to an angle in which the reflection is not visible. There's some good chat here about museum photography and here regarding photographing through/with glass.
Clearly, I could write far more on this subject, but this should provide a sufficient beginning for the documentation of sites and artifacts from antiquity. If you have further questions, feel free to drop me a line here!