dpi (dots per inch) is simply a rating of the horizontal and vertical resolution a printer is capable of. THEORETICALLY, the more dots, the better.
However, dpi ratings can be deceiving and they shouldn't be the sole reason for purchasing one model over another. There are many other factors people fail to observe, such as the underlying technology of the print engine and how it prints.
For example, HP rates a lot of their consumer ink jet printers at 4800x1200 "optimized" dpi. This means that the printer actually has a lower (and unpublished) actual dpi rating and uses a computer algorithm to place additional pixels in the rendered image. It then averages the data to optimize the print quality before it is sent to the printhead. This is very similar to how digital cameras work when they quote an "effective" (interpolated) megapixel rating. The CCD in the camera might be say, of 5MP capability but through hardware/software optimizations produces a quality similar to a 6MP CCD. Epson does the same thing with their 5760x1440 "optimized" dpi printing found on the majority of their current consumer models.
Another factor is the actual size of the droplet the printer's head is capable of producing (these figures are published by some manufacturers, but not all). The smaller the droplet, the more fine detail can be produced. The industry norm seems to fall between 2-5 picoliter droplet sizes (higher-end models generally have smaller droplet sizes). The technologies in the actual inks being used is also important.
The best way to determine which printer looks best to you for your budget is to actually go to the store and try out a few. dpi ratings aside, some printers are better at certain things than others. For example, if you primarily print text and business documents, that 4800x1200 dpi rating will mean nothing to you. Text doesn't need all that resolution to look good. In fact, most ink jet printer drivers limit text printing to say, 600x600 dpi to conserve ink. That extra resolution will actually stand out in graphics and photos, where a lot more detail is actually needed to make the quality comparable to a professional printout.
For your needs, it sounds like you'll be doing a lot of document-based printing and limited graphics/photos. Look for models that have high-yield black cartridges (this is the ink you'll be using the most) and fast text speed. Several manufacturers have models that excel at that, but perhaps suffer in photo output. A good all-around model is the Epson Stylus C84 (being replaced soon by the C86). Good quality text and graphics and reasonably fast, GREAT photo output if you ever need to do it, pigmented inks (they're resistant to smudging and smearing), and individual color cartridges. $100 retail.