If you're looking for an answer just to watch the OVA or the Anime, I won't answer the question.
I will straightforwardly tell you that you should watch the Anime first, the way it was intended.
Then watch the first OVA, and then the Second one. In the Manga, the first OVA is included after the Kyoto arc... but since you said you will probably watch the anime after finishing the Manga, it won't really matter... It's up to you. But I would still reccomend watching the anime first.
Deffinitally watch Seisouhen (2nd OVA) last. It is -after all- the Final chapter in the story.
And now my oppinion. I was declaring that I loved the artstyle of the OVA's more than the Anime. Don't get me wrong, I love the artstyle of the Anime, it's just, that of the OVA seems to be more appealing to me somehow.
Also, the music of the OVA's is brilliant. Here are 4 examples. Two of Tsuiokuhen and two of Seisouhen.
The OVA's are much more darker compared to the actual anime, and are meant for a more serious/older public. Don't expect jolly fanboys/girls to fully appreciate the OVA's. =/
You have to stand open for the harsher OVA's... specially Seisouhen. Okay. the Jinchuu arc was rubbish in the OVA,
but I liked it. I certainly did. Even though OVA Jinchuu was nothing compared to the Manga Jinchuu, I
liked it. And the ending was beautiful. You just have to stand open for it. Because the atmosphere is just so different from the original, yet is the same. =D