I would suggest buying Shea Moisture shampoo they don't have silicones or sulfates and in my opinion leave your hair moisturized. Every time I wash, my hair doesn't feel dry or hard. It's a bit pricey around $10 a bottle which you can find at Walmart or Target, but since I use it once a week, it usually last me a while. It's worth the money. As for the conditioner I use suave naturals its really cheap (less than $2 a bottle and sometimes on sale too) you can find it pretty much anywhere and don't have to worry about using too much. Plus I find it has a good amount of slip. If you have been dyeing your hair often or for years I would suggest a protein treatment. My hair is coarse and according to this site usually doesn't like protein, but since I've dyed my hair for 10+ years and flat ironed it, it does wonders and my hair loves it. You can always do a deep treatment after if it feels a little dry. As for hair type, in your pics it looks like your hair might have been brushed so it's hard to tell what it is tho a lot of ppl here will tell you it's not as important as knowing your properties. I found that knowing my properties help with my hair products such as treatments and conditioners but knowing my type helped with the styling products. But that's just my opinion. Good luck and hope this helps.
curl type: 2c/3a on a good day
med/high porosity & high density
hair strand width: med/coarse
BSL hair & growing