We used the hop on hop off tour - bought online in advance to save money. Stayed in a holiday apartment booked through holidayvelvet - really central - three mins from Piazza Navona (Fico apartment - slept 5 in two bedrooms and one on a sofa bed) but there was handy supermarket for buying bread for breakfast. Use the hot food counters at the back of supermarkets for a cheap lunch. I got some recommendations for good but cheap(ish) eating places from holiday guides.
Many hotels don't have tea/coffee facilities so take a travel kettle if that the case. Make a flask as coffees are quite pricey. Meals are not too expensive suprisingly. Advance book tickets so you aren't queuing for hours