I wouldn't read the manga/source material unless I had to, or I felt like it was the better choice. If I knew that there was going to be an anime adaption of the rest of the series, and I liked the anime adaption, I'd just wait for more anime instead of reading the manga/source material.
There are however times when I choose not to watch the anime first, because I know that the anime doesn't cover all of the source material. For example, I don't want to watch Spice And Wolf, because I know that the anime doesn't cover all the novels, so I'd rather read all the novels first, and then watch the anime adaption of the first 4 novels, or whatever it covers. That way i won't be dissapointed that there isn't more anime, or something like that. It just feels better to read the books before watching the anime adaption... In a way. Note that, I am intending to read the light novels in japanese, so it might take a while before I get that good in reading japanese.
There are lots of anime which didn't get fully adapted into anime that I am going to read the manga of, but other than that... as I said earlier, I think anime is a better medium, in general