I get the “what camera should I buy, but not too expensive” question all the time in regards to people who want to upgrade from a point and shoot to a DSLR (Digital Single Lens Reflex).
Here is my recommendation:
Canon Rebel XSi 12.2MP with an EF-S 18-55mm IS Lens
Canon Digital Rebel XSi 12.2 MP Digital SLR Camera with EF-S 18-55mm f/3.5-5.6 IS Lens (Black)
If you want to go really cheep, buy it used or try to find a new older version like the Rebel XT or XTi. You can usually find the body for around $260 or less and then buy a lens for $100 to get started. Don’t forget that you will need the following that tends to add about 25-50% extra in expenses: at least one or two 2GB or 4GB memory cards SanDisk Extreme III 4GB CF Card, one extra battery (Canon LP-E5 Battery for XSi), a UV lens filter (around $10), a flash Canon Speedlite 430EX Flash), and a camera bag.
Good luck and have fun!