So you want vampire romance but you're new to manga? I was there once, completely intimidated by the sheer volume of stuff. Honestly, just ignore the huge classic titles for now—they can feel like homework. A really smooth starting point is 'Kamisama Kiss'. I know, it's not strictly a vampire story, the male lead is a fox yokai, but the romantic dynamic is exactly what people look for in those supernatural romance stories: a grumpy, powerful immortal being and a spunky human girl. The art is gorgeous and the humor is light. It feels familiar in a good way, like a gateway. After that, if you want the actual fangs, 'Chibi Vampire' (the manga, not the anime) is a good next step. It's older but the premise is charmingly inverted—the vampire girl can't drink blood and is overly emotional because of it. The romance is sweet and low-stakes, and since it's completed, you can binge the whole story without waiting. It doesn't have the intense, dark moodiness that can turn some new readers off.
A lot of folks will push 'Vampire Knight' because it was huge, but I'd be cautious. The art is beautiful and the gothic boarding school setting is iconic, but the plot gets... incredibly messy and the romantic relationships are pretty toxic. It might actually put you off the genre if it's your first. Better to build up a tolerance for that style of drama later. If you finish something like 'Kamisama Kiss' and think 'I could handle more angst and a darker aesthetic,' then maybe circle back to it. But starting there feels like learning to swim by being thrown into the deep end of a very dramatic, rose-petal-filled pool.