Rome for the first time

Suggest you take it easy as Rome is a place you can walk yourself in. Buses and the metro is the fastest and most efficient way to get around. Learn how to negotiate the mass transit system to save your legs.
We'll be there in April for our 2nd Easter in 3 years. It's important to stay in a centralized location.
I'll leave the itinerary for someone else. But you'll want to get reservations for the Vatican Museum and end up in St. Peter's. Pantheon is another favorite travel site there. Last year, we enjoyed the Borghese Gallery. Of course you'll want to see the Colliseum and surrounding sights.

A good general overview would be to take the hop-on-hop-off bus tour - which goes past the most popular sites.
A beautiful view of Rome is from the Monumento Nazionale a Vittorio Emanuele II , it is near the forum and the coliseum. There is an elevator that goes to the top and your have 360 degree views of all of Rome. It is amazing.... stay up there as long as you want and take photos of the city.
I was able to zoom in on great pix of St. Peters and other famous buildings.
I always try to stay near the central train station because it is close to the transportation connections.
I usually buy a 3 day Roma Pass which is admission to many sites, bus, metro etc.
(I'm a duffer too)
Hope you have a wonderful trip.

There are some sights in Rome--if they interest you--for which you'll need to investigate advance-purchase of tickets either because they sell out or because on-site ticket lines can be extremely long. So check your guide book and other sources and decide which, if any, of these deserve a place on your itinerary:

• Colosseum (long lines)
• Colosseum underground tour (sells out)
• Vatican Scavi tour (sells out)
• Vatican Museums (incl. Sistine Chapel; this is a mob scene; investigate early-entry options)
• Borghese Gallery (pre-booked tour mandatory)
• Domus Aurea (sells out; open weekends only)
• Pantheon now requires tickets (I suspect lines may be significant)

I don't remember what the ticket situation is like at St. Peter's itself.

Frances' advise to go to top of the Victor Emmanuel is right on. The view is the best in Rome.

The Colisseum, Forum, Palatine Hill will take up close to a day, in energy if not time. I spent close to five hours and the time flew by, but I like to linger. Vatican Museums and St. Peters will take up another day. Find a way to get to the Borghese Gallery. Rome is exhausting, my feet hurt for ten days after I came back from Italy and I'm in my early 50s! But I am a nut that runs myself too hard. Use your head to figure things out, not your feet like I did. Figure out the bus lines, there are some that run along Via Nazionale to get from Centro Storico to Termini that can useful if staying near there. Don't miss the Spanish Steps or Trevi Fountain, also the Pantheon. Three nights is not enough, buy plan ahead to make the most of the time you have.

Also note that there are well-labeled photo murals on the roof of VEII monument, so you know what you are looking at.

Pantheon now requires tickets (I suspect lines may be significant)

I know that's being discussed by the ministry but I haven't heard that entry fees have been put into play yet. Soonest I read that it might happen is 2018, unless I've missed something (always a possibly). Anyway, very recent visitors don't report having had to pay any fees, and they aren't noted on any of the Roman tourism websites so far.

Sorry about the misinformation. I thought I had read on this forum that someone had been to the Pantheon and found tickets already required. I guess I misinterpreted or am mis-remembering. I should have checked the official website, which still shows "free entry".