If you fly you will miss the most amazing landscapes.
You can do the whole circuit by bus. Not very confortable but not impossible.
Note that bus leaves very early in the morning. And, if you wish to chose a good seat (ex. the only seats with enogh room for long legs are the two just beside the front door) you must go at the bus station before they open the gates.
When they see you are a western tourist they will open the gate and allow you to find the bus and chose your seat beafore the local people are allowed in. This is a gret help. Unfortunatly it doesn't happen in southern Ethiopia and there you should run at the gate opening, along with hundreds of fitter ethiopians to reache the bus.... good luck!)
In Lalibela Asheton Hotel is quite good, single or double romm is 100 bir (try to bargain if you are alone. I payed 80 bir)
and it is quite close to the bus station. Note that in Lalibela there are many budget hotels but two kilometres down the hill from the bus station and then, when you leave you must climb two kilometers vcarrying your backpack. No taxis in lalibela, only jeeps to visist churches around. Dont miss Ymrehanna Kristos, maybe the most beautiful church in all Ethiopia - 400 bir (but jepp can host up to 6 people).
From Lalibela to Axum is a long way because there are no bus on the direct road. 6 hours from Lalibela to Wolodia, then & hours to Mekekle (north of Mekele Tigrai churches and wonderful landscpe. If you like frescos dont miss Chelekot Selassie Church (17 Km from Mekele, you must hire a minibus by yourself. 200 bir).
From Mekele you can go stright to Axum about 6 hours.
Axum (for me a bit disappointing) Africa Hotel is very good, also restaurant.
From Axum to Gondar the landscape is amazing. A long day journey by jeep or by bus (note that the bus leaves at 6 AM from Sire so you must go to Sire the afternoon before and sleep there.
In Gondar stay in Pension Belaguez, Excellent. Also very good food.
From Gondar, if you like architecture and frescoes (best old ones!) dont miss Debre Sina Church in Gorgora (a day trip from Gondar).
From Gondar to Bahar Dar is a short journey by bus.
In Bahar Dar, Bahar Dar hotel is quite good . They have the best restaurant in town; very good fish. Lonely Planet says it is noisy but it is OK because after 10 PM it is very quite.
From Bahar Dar there is a whole day bus journey to Addis Abeba.
In Addis Abeba Taitu Hotel in piazza is the best budget and good atmosphere (is the oldest hotel in AA, built by Empress Taitu; expensive double rooms in the historical building around 160 bir, cheap rooms with share bathroom behind, single 63 bir double 88.)
Exchange rate i 14 bir for 1 €. In the souvenir shops in Churchil Avenue (not far from Piazza) slight better exchange rate.
Enjoy it.