Photo printers usually use single inks for single colors, instead of the big catridge for all the colors like a normal printer, higher the dpi the better, and generally those "all in one" printers arent a good choice. Also make sure to get the right photo paper for what you want, there are different glosses on paper.
I don't want to get anything that will be over $250.. So I think that should give me a lot of options. What is a good dpi? For both color and black&white ?
At that price range...
* It will be difficult to find a printer with an archival ink set. I have prints from my old Epson 825 that have turned color in a year of two of constant bombardment from fluorescent lights in my office at work.
* You most likely won't find a wide printer for larger than 8x10 prints
* Selection of art paper (many are too thick) is very limited
* In my experience, B&W prints usually end up with some sort of color hue
With that said, the $250 is best put towards sending your prints to MPIX (or some online photo print agent). The overall hassle will be less and the quality will be LEAPS and BOUNDS better than what is achievable from a $250 photo printer.
I've had wonderful service out of MPIX. They have a selection of papers and sizes. I also get my prints well packaged within just a few days.
Find and use a good lab in your area! Unless you are printing a lot a photo printer is not worth the expense.
Invest in a monitor calibrator -and a good monitor if you don't have one of those- and photo editing software -if you don't already have a program. You'll be much happier in the near and long term.