short trip

If you depart Wed morning, you really have only 3.5 days (Sat PM, Sun, Mon, Tue). That's a decent chunk of time for Rome's basics but you have no time for anything else. At most a day trip to Orvieto, if too many Roman ruins burn you out.

Museums If you want to visit the Vatican museums, plan to go on Tuesday or Wednesday. They are closed on Sunday so Mondays are crowded. It's often worth paying the fee to reserve tickets so you don't have to wait in the security line, there's a separate, short or nonexistent one for reservations. If you want to visit the Borghese Gallery reservations are a must.

You may want to get the Roma Pass to avoid the lines at the Colosseum. If you don't, try going to the Forum first, the lines may be much shorter (it's a combined ticket).

Rick has several free audio tours (about 45 minutes each) that you can download. I've enjoyed them. Be sure to print out the maps that go with them. If you use them, plan on the Jewish Ghetto and then the Trastevere - they are next to each other. On Saturday, many of the shops in the tiny Ghetto will be closed.

I find it easy to get lost in Rome and somewhat hard to find buses. Get a good map and plan in advance how to get from place to place.

Since you really only have Sunday, Monday and Tuesday I would pick a different area for each day and get a good guide book, like Rick's "Rome" and choose the sites that interest you in that area. You could do historical Rome one day: Coliseum & Forum area, Vatican, one day, etc. Rick has two pages in his books with his ratings of the top sites. This would help you choose. I would also recommend his walks. The evening walk on the day you arrive would help keep you awake and get over jet lag.

For starters do these in the monring and start to add other things that interest for for the afternoons
1 day - Vatican
1 day - Coloseum, Ancient Rome
Full Daytrip to Orvieto - easy train to and from Rome.