Also, should I avoid "Actual" vampirism to keep face same and use animal meats (she drinks blood of animals, and clearly says so) as "blood"? Maybe Vampire dust would substitute for Vampire blood?
I'm not familiar with Bloodrayne, but for vampires I find Nightblades seem to work better than other builds: Stealth, Illusion, backstabbing. Vampires get a nice boost to both Illusion and Stealth. You'll need a secondary combat style for when stealth fails- Destruction is traditional for nightblades, but conjuration or sword and board would work.
Vampire Armor (red variant) is the most befitting set i can think of for Rayne. As for weapons you cant get guns or her awesome blades so Ebony Daggers are a good substitute
If you are not on PC I would suggest avoiding actually becoming a vampire as any option of being hot is gone at that point. In fact, it seems difficult to even make an attractive female on an unmodded game.
As for equipment, it looks like you are referring to the Bloodrayne from the first bad movie. If so it is difficult to find a suit that looks like the one in the pic. But she also wears Skyrim-looking fur armor a lot during the first three quarters of that movie. I have done the same thing and used that armor well smithed for much of the game. She now wears Nightingale armor sans hood and since she does about 400 damage per attack she often just wears the boots, guantlets and jewelery, with the Diadem of the Savant. Then when she needs it I got the cuirass, and thieves' guildmasters hood hot keyed and her AR jumps a whole bunch as the 25% bonus for Custom Fit applies. I think the Nightingale armor looks a lot like her outfits from the original video game and some in the second movie.
That said, you can really start your character based off Bloodrayne and wear different outfits that suited the situation which is essentially what she does in the movies and games. I Like dual wielding Skyforge steel swords as I don't have any mods but face and body mods. Ebon daggers are no bueno as they have slow speed, unless that is fixed. Still I think the Ebony Swords would be more appropriate if you wanted to go for that many smithing perks to improve them, otherwise Skyforge Steel with steel perk is best for perk cost/damage ration and looks in my opinion.
For some build advice, I would suggest that you get started on the MQ fairly soon, at least by when your onehanded is 30, then you can easily veer off at some of the early points. Then get yourself to one of the Elemental Fury word walls, I find the one north of Meridia's shrine the easiest to access. Once you get that shout activated, especially once you have 30 skill and Dual Flurry perk, you will never have an opponent who can beat you in melee. At that point I even abandon blocking when fighting dragons and just run up to hit them in the nose....