I would begin with SCIV as a starting point. My reasons being that SCIV is my favorite game in the series, a sequel in its style has never been made, and the formula has room for iteration and improvement.
For improvements on the formula, I would focus first on restoring the difficulty balance of the game while retaining the free form controls.
The dark, gothic horror atmosphere of the Castlevania games has always been a huge part of its appeal for me, so I would ensure to keep a fitting atmosphere throughout.
I would keep the Stoker Dracula as the primary villain, but I would mix his character with the historical Dracula. I think the world that Vlad Tepes lived in makes for a great origin story setting for the Stoker Dracula. Dracula was a brilliant man, who mastered every discipline he attempted to conquer, and was considered a master alchemist. What drove him down the path to Scholomance? This is what I would want to see as a long time fan of the legendary character.
I would also like to play as Dracula! The iconic lord of the vampire himself, give him a lead playable role in one of the games. I would love to play through a set of dangerous trials within Scholomance that test the worthiness of an aspiring vampire lord candidate.
I would make one game that's like a traditional Castlevania- you play as a vampire hunter that fights through the countryside and into Dracula's castle. But I would also make a game that takes place in Scholomance and you play as Dracula, so you can see the experience from the opposite point of view.
I would have a set of "regular" levels, but I would also create a lot of optional sub-levels that test some specific skill. Maybe you are forced to fight a buffed up version of a previous boss, or two of the previous boss at the same time, or perhaps you are given a short but difficult platforming obstacle course.
and I could go on forever...
I will be answering this question in the form of a playable demo soon.