We are staying at the Eco Hotel in the Aurelio district of Rome. Does anyone have any transportation suggestions for cost conscious travellers from the airport to this hotel/area?

Directions are on their website. I understand being cost conscious, but this hotel is quite far out. There are other options to stay more central if your decision is based on price.

>>Option a) Line FR1 (every 15 minutes) from Fiumicino Airport: get off at the Trastevere station. From here, take line H (towards Largo dei Capasso) for 9 stops. Get off at Dei Capasso (end of the line) and continue on foot for 300 meters to Via di Bravetta 91.<<<

That is likely the most economical train option (train part to Trastevere is 5.50€ - don't know how much line H would be, but probably just a few €), but it would be easier to book a shuttle such as Rome Shuttle Limousine for 40€.
http://www.romeshuttlelimousine.com/FiumicinoE.htm

You stated on another thread you only have 9 days and 3 cities. I would stay closer in so you aren't using so much time getting to and from your hotel to the things you want to see.

Although it is more expensive, after a long plane ride, it is so much easier to take a cab to one's hotel. Did you say on another post that you have an 8 y.o. with you? S/he is going to be exhausted also-can you carry your luggage and a child up and down train station stairs after an extended sleep-deprived trip as you try to figure out directions in Italian?

Or, take the train to Trastevere and cab from there. Might save a few bucks that way.

ok, it is always good to get advice from people in the know. sometimes it's easy to get so cost conscious that you tend to forget all the other logistics involved. We have a great price for what seems like a nice, clean place to stay - any other options closer to the center?

You will get better suggestions if you tell us how much you want to spend per night, and how many people/rooms.

Or do a search here for Rome Budget Hotels for lots of suggestions.

From another post, Banff's party is "2 adults, 2 kids" though no idea of ages of kids.

I agree that this location looks very far away from the center. Your money savings may be a waste of precious vacation time traveling to the center. If your children need a break, it will be a big deal to return to your hotel for a rest or to relax a bit before dinner.