OMG where to start.
Italy is huge. Don't try to cover too much ground in one visit or you'll waste too much time in transportation and just wear yourself out. Just remind yourself that you'll be back many more times, especially now that $400 round trips are possible.
Lots of others will have good advice, I'd suggest a couple random things:
If you want to go to Venice, you need high speed express train to get there. Look into buying Italo train tickets in advance.
http://www.italotreno.it/en If you can buy them early, they're cheap ($40 one way) and Italo trains are extremely fast and nice. Rome to Venice is about 3 1/2 hours because the trains go about 200 mph.
(Spend a little time on Italian and French trains -- fast, clean, quiet incredibly cheap -- and you come back to the U.S. and realize we live in a 3rd world country.)
Rome-Florence is on the regular italian train system (trenitalia) and you can probably buy those when you get there -- that one's about 2 hours.
If you're going Rome to Florence and you'd like a gorgeous stopover, I'd recommend Orvieto about an hour north of Rome. A little town high on a plateau of tufa (volcanic stone). Because it was protected, various popes would go there when things got too dangerous for them in Rome, so the popes showered money on the place. One of the most magnificent cathedrals in Europe, a World Heritage site perfectly preserved and untouched by war -- and just a lovely little town to walk and enjoy the views. The fresco cycle by Luca Signorelli is considered one of the 5 or 6 most important in Italy -- and wonderfully preserved -- but it's not besieged by tourists like most of others.
I love Lucca, I keep going back. Lucca is only about an hour on the train from Florence. Just a gorgeous little city, beautiful architecture everywhere (San Michele in Foro and the Cathedral are two of the most beautifully decorated Romanesque churches in Italy). The city wall is a big wide thing and it has a bike/walk trail, and you can rent bikes. If you go to Lucca on a weekend in nice weather, it'll be thronged with happy Italian families day-tripping there, soaking up the sun, walking the walk, just hanging out. Just a wonderful sweet experience.
Pisa is on the same line and also a wonderful old place. Virtually all the Italian cities have gorgeous architecture and beautiful squares and wonderful churches and monuments. But Rome and Florence have really gigantic impressive monuments -- it's the scale that sets them apart.
Rome is Rome. You could spend a lifetime getting to know it. There are 500 artistically/historically important churches in Rome -- 500! I'm not sure I would recommend the Vatican/Sistine chapel complex for your first trip because it will eat up an entire day basically being in rabbit chutes with other tourists. (St. Peters doesn't have huge lines unless there is a religious holiday -- but there are lots of those in Italy.
Instead, see some of the 1000 other things in Rome that don't come with 4 hour lines. Like Bernini's bridge outside the Castel Sant'Angelo. Or the Spanish Steps -- yeah, touristy but such a fabulous place to hang out. You have to see the Piazza Navona fountains and the Fontana Trevi but try to see them very early in the morning or the evening to experience them without 10,000 people crowding around. Same with the Pantheon -- go in the morning when it opens. So many of the best things in Rome do not require a ticket.
See "Roman Holiday." It's a great movie -- but what's cool is all the places that Gregory Peck and Audrey Hepburn visited are still there and it's not a bad starting itinerary for a tourist. You follow their path and you'll have a good introduction to Rome.
