I have not done this; these suggestions are the product of Internet research only. I hope someone with actual experience will be able to confirm or correct this information.
Rome2Rio.com is a good place to start with questions like this. It will usually tell you what your basic options are. Unfortunately you cannot trust the fares, travel times or frequencies it displays. Instead, you must drill down to find the name of the company operating each transportation leg and go to its website to check schedules. In this case Rome2Rio says you can start with a Metro ride from T4 at the airport to Nuevos Minsterios, where you can pick up a local (Cercanias) train to Aranjuez. The Metro runs frequently; you'll be taking Line 8. You can find the Cercanias schedule here: http://www.renfe.com/viajeros/cercanias/madrid/index.html. Use Nuevos Ministerios as the origin. There seem to be at least two Cercanias trains per hour, sometimes as many as four.
I don't know that you'll find a place to store luggage in Aranjuez.
Going on to Toledo will be trickier. The company AISA seems to run just five buses a week (probably Mon-Fri) at mid-afternoon. The other reasonably-inexpensive option is to take the train back to Madrid's Atocha Station, walk to a different part of the same station (listed on schedules as Puerta de Atocha) and take the ALVIA to Toledo. Ideally you will have bought both tickets (Aranjuez-Madrid and Madrid-Toledo at Aranjuez; that will allow you to avoid the possible lines at Atocha Station. Or you could use a ticket machine there, but first I think you have to find the right kind of machine for tickets to Toledo. Be aware that afternoon trains to Toledo run only every 1 to hours.
I believe it's just under 30 miles from Aranjuez to Toledo. This might be a time to throw money at the problem and take a taxi. But this is adding up to considerable transportation expense, and if you're arriving on an overnight flight that day, I don't know that you'll get much, if anything, from your time in Aranjuez.
If the plan is to take the train back to Madrid before going on to Toledo, the logical way to handle you luggage is to store it at Atocha. That would mean taking the train (rather than the Metro) from the airport to Atocha Station. I've never stored luggage at Atocha, so I don't know how long you'd need to allow for drop-off and pick-up.