Switching from reddish brown to bright red. Hair lightening question!

So I've had red/brown hair for a couple of years. Here is a picture of my current hair color. This is my natural hair color in bright sunlight. (sorry for the Nigel :P )

So I'm goin' RED. I got Arctic Fox and I think I figured out the color combo (Poison with just a teeny little bit of Violet Dream to cool it since I'm cool-toned.)

The ideal color I'm going for is like this or maybe this.

I DO NOT want something like this

So my question comes down to lightening. I don't think bleach is the answer because it'll be too neon. But I don't think going over my current color will bring out the vivid, the brown would just muddy the brightness.

So I don't know if I should use a developer or a color stripping kit or what. So any tips are appreciated! :)

Please note: I'm not doing a salon. I'm broke. Non-negotiable.

EDIT: I've been trying the vitamin c treatment and it's just not working, unfortunately :/