The recording you linked to sounds somewhat Germanic--in fact, to me it sounded as if he is using an uvular r instead of a trill or flap.
But I wouldn't worry to much about getting the pronunciation exactly right. After all, there are no native speakers of classical Latin alive today. Contemporary attempts to reproduce ancient Roman pronunciation are nothing more than educated guesswork based largely on very crude descriptions of Latin phonemes in ancient sources, which of course didn't have the International Phonetic Alphabet at their disposal to render Latin pronunciation with the precision that would satisfy a modern linguist. I suspect that if we were
able to hear an ancient Roman speak, it would sound much weirder than, and very different from, the recording you linked to.
You might want to get a copy of this book if you don't already have a copy, which discusses the evidence and makes some recommendations:http://www.amazon.com/Vox-Latina-Guide-Pronunciation-Classical/dp/0521379369/ref=sr_1_1?ie=UTF8&qid=1377957982&sr=8-1&keywords=vox+latina
In general, though, your time would be better spent learning grammar and vocabulary, and above all reading, than attempting to improve your pronunciation.