Changing money for Ethiopia. Where can I get the best rates?

Well the best rate is on the black market, which does exist. However, this is illegal. Your best bet is a bank, and all banks in Ehiopia have the same rates.

From Wikitravel:

Any commercial bank in Ethiopia can change cash. The rates are the same everywhere. There are dozens of commercial banks in Addis, including in the Sheraton and Hilton hotels, and in the corner of the baggage claim hall at the airport. Most cities and towns that tourists visit will have at least one commercial bank, except for villages in the Omo valley. US dollars, euros, or British pounds are the best currencies to carry.

It is illegal to change money on the black market and the rates aren't much better than what you can get from the banks.

The Lonely Planet has a good article on money costs in Ethiopia.

According to the article, for ATMs:

Bigger branches of the Dashen Bank in Addis Ababa, Bahir Dar, Gonder and Mekele now have ATMs that accept international visa cards. The service is likely to expand to regional cities and even to other banks quite quickly. Note that Mastercard, Solo, Cirrus or Plus cards do not work in any ATM.

USD or Euros?

As with many African countries the US dollar is the preferred foreign currency in Ethiopia and although the euro is growing in popularity not all banks will accept it; therefore you should still pack a wedge of greenbacks.

Personally I almost never get cash in advance, except when I know it's going to be tricky in the country (eg Japan, before 7-11 installed ubiquitous ATMs there that accepted foreign cards).