Reddit reviews Hand Dyeing Yarn and Fleece: Custom-Color Your Favorite Fibers with Dip-Dyeing, Hand-Painting, Tie-Dyeing, and Other Creative Techniques

For yarn, Knit Picks Wool of the Andes is probably the cheap starting option. I really like bare Felici. Superwash wool tends to suck up dye faster than non-superwash, so it can be a little easier to work with (plus, harder to felt!).

Be sure to check out the safety thread on the sidebar - you should have eye protection, a mask, and gloves.

I really like the book Hand Dyeing Yarn and Fleece - it's a great beginner's reference for dye techniques, and I use it for color inspiration if I'm in a rut.

Some other things I've found useful (as an experienced-ish hobby dyer):

• Borosilicate glass beakers - for measuring, or for dissolving dyes in hot water.
  
• A small saucepan for heating up water to make dye stock (might be a non-issue if you're working in a kitchen, I dye using a portable burner in my basement)
  
• Plastic squeeze bottles - for squeezing dye when hand painting. I've been using Wilton's cake decorating bottles that I got in a multi-pack from Michaels.
  
• Scales! Both a food scale for yarn, and a small/jeweler's scale for measuring out dye powder.
  
• Tiny spoons to handle dye powder, and small utensils for mixing dye powder in water.
  
• Citric acid! Vinegar works, too, but a little goes a long way with citric acid and it smells so much better.
  
• Synthrapol - not truly necessary, but can be nice to have. It's a detergent you can use while soaking yarn to get out oils and such that could mess with the dye absorption.
  
• Spare bowls or tubs for soaking and rinsing yarns.
  
• Salad spinner - nice to have for spinning out extra water after dyeing and rinsing yarn/fiber.
  
• Plastic wrap, if you plan on hand painting and steaming anything. The wider the roll, the better!
  
• Extra bottles/jars to store dye stock, if you pre-mix dye stock. Some people just mix up the dyes they'll need that day, but I prepped stocks in advance and store them in mason jars.
  
• Oral syringes for measuring out pre-mixed dye stock. Depending on how precise I'm being and how much yarn/fiber I'm working with, I'll use syringes anywhere between 3ml and 60ml.
  
  I don't have any strong opinions on dyes - check out Paula Burch's website (linked on the sidebar) to get an idea of the difference in the dyes. Her site can be a pain to navigate, but it's a wealth of information. I primarily use Lanaset/Sabraset dyes (same dyes, name just depends on the retailer). They generally have the best ratings for colorfastness, but they're supposedly a little more finicky than some of the other dyes. I haven't had any trouble with them, but I don't have enough experience with other dye brands to really compare them. I prioritized purchasing dyes that are "pure" rather than a mix of multiple colors, per information on Paula's site.
  
  I've purchased my dyes from Pro Chemical & Dye. Their starter kits would be my recommendation; that's how I got started. Dharma Trading is the other big dye retailer that I'm aware of.
  
  Possibly helpful note: I mix my dye stock to 1%, or 1g of dye in 100g/100ml of water. For reasonably saturated colors, you'll usually use 1% "depth of shade", which is the ratio of dye to yarn/fiber. So, if you have 100g of yarn and want 1% depth of shade, you'd use 1g of dye - or, in the case of pre-mixed 1% dye stocks, 100ml of your dye stock (which I measure with the oral syringes). Since you use so little dye per 100g of yarn, it means that the 10g of each dye color in the starter kits can go a LONG way!