Be aware that different missions archive data in different stages of readiness. Also, your instructor and TA may be vell versed in handling some types of data, and completely ignorant of others. You are facing exactly the same problems that any professional astronomer faces in dealing with a new kind of data set. You should read the page on astronomical instruments . This will give you some idea of what types of data are available in the archive, and may help you decide what to investigate.
Projects Compare the coronal and chromospheric spectra of an active star and an inactive star.
Determine the power-law slope of the Crab nebula spectrum. Use X-ray, UV, and IR photometry. Determine the temperature of a star from its spectral energy distribution. Measure the radius and surface brightness distribution of a galaxy. Compare the UV spectra of a sample of QSOs, Seyfert I, and Seyfert II galaxies.