The endings are essential - in Latin the word order is free, often exactly the opposite of what you would expect in English. In English, word order conveys a lot of the meaning, while Latin uses the different forms of the words to do that. If you don't know how Latin does that, you will make assumptions based on the word order which will quickly lead you down a wrong path. You can learn the endings by reading, absolutely, you don't just have to memorize paradigms - but as you are reading, paying attention to the whole word, including the ending, is ESSENTIAL. Word order is important in English; word endings are important in Latin.
Some Latin textbooks present Latin with English word order, which can lull you into a false sense of security. I'm not familiar with Ecce Romani so I don't know if it is a textbook that falls into that dangerous trap or not!
As someone recommended, Eutropius is a great text to read - you can find various editions listed here:http://ilovegooglebooks.blogspot.com/search?q=eutropius
Some of them have dictionaries built into the book; vocabulary is a huge challenge when you start really reading Latin, so using a reader that has a complete glossary can be a really good choice.