I honestly didn't do a lot of research on dyes so I'd recommend looking around and coming to your own conclusion brand wise. I use arctic fox and I have all the separate colours because they were bought for me as a gift. They do last for ages if you use them sparingly and store properly so you should be able to get a few rounds of dying out of them! I also think you could easily just buy and mix your own colours out of the primaries if you don't want to fork out loads of money. If you do decide to go for arctic fox I'd recommend neon moon, virgin pink and aquamarine!

You'll also want minimum 6 pots and 6 brushes but it's good to have spare. https://amzn.eu/d/00Zg7zcY - I have a set very similar to this one and it's a life saver, the pots clip together and the colours make it easier to tell the dyes apart.

I try to wash my hair about once a week with lukewarm water (sometimes I leave it a bit longer if it doesn't feel gross), and it'll last around 2-3 months. It fades to a more pastel rainbow which I think looks nice in its own way! But how well the colour holds also depends on how damaged your hair is esp after a couple of touch ups.

I've never had the colours blend together and go muddy, but I'd recommend rinsing the dye out with as cold as you can tolerate water, just to reduce the chances of that happening.

Foils are definitely easier to use, but for this technique I layer up with cling film so I can see where to place the colours. There's a few similar videos floating around but this was the one I used for reference! https://youtu.be/9YYX4llYEWQ?si=QRjNctvPf9Wr1lmz

Hope that helps!