The Sakura Taisen series is really hard to recommend, but it is safe to assume that if you liked what you have seen already you will probably like it all.
I did not watch too much of the animated series, but I really appreciated the quality of the animation, some of the best I have seen in Japanese-made stuff.
Even though it takes place way later in the series, I think the movie is a good way to start off, and I liked it the most. It leads up to the fifth game anyways, so that could be cool for you.