Adobe Illustrator is vector based. You should convert it into some bitmap format (.jpg, .png, etc) with 300dpi.
You can print directly in AI to the size you want without conversion to a raster. AI is a mathematical based artwork program and therefore doesnt require you to set any DPI at all.
Just make sure your artboard and artwork is set to the print size you require...thats it.
If you are going to convert an AI file to a raster, ensure that you only save it in 3 formats: BITMAP (BMP), PNG or TIFF as they are uncompressed and will preserve all the quality a vector drawing is capable of providing.
DO NOT USE JPEG!