Ugh, after I made our train reservations, I noticed that the train station we will be going into Rome is the Roma Tiburtina. Is this a problem? Can we get to our apartment by metro from here (Piazza Del Popolo)?

Yes no problemo - metro goes everywhere just like from Termini, the hectic main station - I love Tiburtina because compared to the zoo at Termini with zillions of tracks and platforms Tiburtina is relaxed and easily manageable. Metro right from station - Tiburtina is only a few miles from Termini so just as good for getting to many hotels.

If you have luggage, I'd say take a taxi.
We taxied from Roma Tiburtina to our hotel near Piazza Repubblica last May, and the fare was 9 Euro.
Piazza Del Popolo is a bit further to Roma Tiburtina (than Piazza Repubblic), so may be a few euros more?

Thank u both! On to the more enjoyable part of planning

You've got to change metro lines at Termini for Flaminio-Piazza del Popolo, which all adds up to about twice the distance a taxi would travel. Depending on time of day, the metro might be faster, and changing at Termini isn't quite as horrid as starting your metro journey there - but it's still Termini, which isn't Europe's most pleasant tube station.

With bags, personally I'd hail a cab. Which is also a more pleasant experience at Tiburtina than at Termini.

I actually preferred Tiburtina over Termini...much less activity, and it was pretty cavernous when we were there in February. Granted, that means fewer places to get a snack and it's a bit away from things, but if you like that, then it's no problem.

You can also go outside, hop on bus 490 (departs every 8 minutes) to Piazza del Popolo.

Kybourbon, I think the bus would be best! We are 5 so I suspect we'd need two taxis. Thank u!