Trying out the collection sounds like a good bet. You can see if DMC1 is for you, and if it feels a bit dated (the combat is not nearly as complex, but it certainly makes up for it in just about every other department), then you can move right along to DMC3, the height of the series if you ask me.
As someone else said, if you take a liking to DMC3, you'll only have more to love in the combat DMC4 has to offer, even if some other aspects of the game take a hit.
What happened to survival horror? Ironically, it did not survive - TheCyborgNinja