Jeroen is right, shoot in Raw and convert to other formats as required.
Jpeg is only an 8bit format as your camera saves any data that won't fit inside the 8bit file is dumped. Jpeg tries to compress more data than it should be able to hold, the problem is it's a 'lossy' compression and can add compression artefact's.
By comparison any Raw file is at least a 12bit format (often 14bit these days), every bit you add from 8 to 12 doubles the amount of space for data in the file (note it may not be filled, it depends on the subject, but this space is available for editing into). Raw files contan ALL the data from the sensor.
Tiff files come in both 8bit and 16bit formats, 8bit has the same restrictions as Jpeg, but it handles the compression losslessly. 16bit can be thought of as 'infinite' for a single image.
You may get 'improvements' in a Jpeg processed in a larger bit depth file, as the edited data can move and be saved in the larger format, but the data won't be original as saving in Jpeg 'dumped' that.
Chris