Pellets, crumbles or mash is just a shape it is not a type of feed. Some people prefer one shape over another because the chickens waste less but it depends on the type of feeder you have and your birds and your personal set up.
This thread has a good pic comparing the three shapes:
https://www.backyardchickens.com/t/...-feeds-are-good-for-the-chickens-see-the-pics
I would be more concerned about the type of feed and it's nutrition content. A lot of the stuff you mentioned should already be in your feed. Worry about what is in your feed first and shape as a secondary concern. If you get a complete feed then you only need to give feed. Make sure to read the labels. You want to pay attention to the protein and calcium content and find a food that meets the needs of your individual flock. There are a number of choices and not all feed is for all birds.
Layer feed is commonly fed to laying hens. It generally comes in all the shapes mentioned above. Layer feed is made only with frequently laying hens in mind and has extra calcium. Young birds CAN NOT eat this. It is too much calcium and is bad for them. It is also not great for roosters or any other non-laying birds.
If you have all laying birds a layer may be a good choice. If you have a mixed flock then a grower or flock raiser may be better, This feed has lower calcium and generally a little higher protein. Because it has lower calcium you will need to supply your laying hens with a extra calcium source separate from their feed. Oyster shell is common. They will regulate their own calcium as needed if it is separate.
Grit is just little rocks. If your hens free range or has access to lots of dirt then they will find it on their own. If they are confined in a smaller space you may need to provide.
People tend to have very strong opinions about their feed choices so its always good to do some reading and decide what really works for you -- medicated or non medicated starter? layer or not? organic or not? soy or animal protein? lol What is "best" is hard to say as it is going to vary from person to person.
I personally feed a mash. It is not my favorite shape (I would probably pick crumbles) but I choose to feed a 20% protein organic grower feed and it is locally only available in a mash. I feed this with oyster shell and grit on the side (very small yard). I would rather have my preferred nutrition content than preferred shape.
Good luck!