Just got back from Rome a few weeks ago.
If you can change your booking, I'd go with an apartment over a B&B. They tend to be cheaper and you will have a kitchenette with can be a huge money saver.
If you have a fridge in your B&B room, you can at least manage breakfast and maybe some lunches. And carry a small snack with you so you don't end up being forced to eat at expensive places. (Anything on a street with a major tourist attraction is going to be pricey. Always go two streets over.)
I too recommend Rick Steves. He has a great app, and through that you can download audio versions of most of his tours, for free. Bring headphones (with a splitter so you and your wife can both listen) and walk yourself through the major sites. We did his colosseum, Forum, Pantheon, and Sistine Chapel. We also did his Pompei tour, but on a budget, getting there is probably out of the question.
We were worried about lines. We had *no* lines, likely because it was offseason. When I say "no lines", I mean none. We waited behind 1 person to get our colosseum tickets, and one party to get into the Vatican Museum. This was the week of American Thanksgiving. If you are there off season (and not Christmas, as I'd guess it is busy during that time), I wouldn't worry about lines.
There are tons of churches with great art, and they are free. If you like Bernini, you can do a search to fine places that have his works. Free (though you can throw them a Euro if you feel so inclined).
We did the math and based on what we wanted to see, the Roma pass was a screaming good deal. Good for 3 days, it gives you free admission into 2 sites, and a discount on everything else (for sites covered, see their website). it also covers all metro rides for those three days. If you get the pass, be strategic in your planning. Go to the most expensive 2 sites first (as the first 2 are free) and also do your heavy public transportation activities on those days.
Don't drive. At all. We walked a ton, even with 3 days of "free" metro. It was part of the experience and allowed us to pop into churches, wander by excavation sites, and just sort of feel Rome. It's a great city for walking. And I'm not an American who is scared to drive overseas. I live in Europe. There's just no need to drive in Rome.