So I'm pretty set on doing my hair in layers (red on top, purple in the middle, and a blue velvet color on the bottom) which is all fine and spiffy but....I am sorta running out of funds.

Since I'm bleaching my entire head I will most likely (99.9% chance of) using Special Effects so all color names are from that brand.

I'm pretty set on blue velvet so I get a dark, almost black but noticeably blue color.
as far as red I will probably use, Hot Lava, Blood Red, or Nuclear Red

So...which could I mix to get a nice even purple thats not too red or too blue?

Ooh. I did a combo like that. Fushia/pink on top, purple in the middle, blue on the bottom. It looks really nice :)

Those reds are a bit orangey, if i remember correctly, so the purple might come out more browny and mucky looking. Try to find a red with more pink in it.

You can always just mix a teensy bit of each and do a strand test to see if it comes out a nice purple :)

hmm how about cherry bomb or atomic pink dyed on darker hair?

Blood Red should work fine. Devilish is pretty neutral, too. Cherry Bomb will work, but with any of these, only add a tiny amount of blue at first. You can always add more, but it's hard to "undo" with more red, since Blue Velvet is such a dark color.

I've used Atomic Pink over purples and reds and it lends a really interesting color. It looks especially nice with Deep Purple.