Answers to your questions might be better if you can describe what you are going for. You mentioned Chicago deep-dish pizza. Is there a Chicago thin-crust pizza that you are trying to emulate, or some other pizza that would be at least fairly well known by other people on the forum?http://slice.seriouseats.com/archives/2008/01/a-list-of-regional-pizza-styles.html?ref=skybox1
For sauce, you can do whatever you want. Whatever taste you are going for and whatever floats your boat. Some folks might just put tomatos or a plain sauce on their crust. Escalon 6-in-1's are a good product. Traditionally, people who have made this type of pizza in the past have generally spice up a basic tomato sauce (puree, paste, etc.) with herbs of their choosing. Sauce is probably the hardest thing on which to give advice because it tends to be the most personal thing on a pizza. I'll go ahead and give you a recipe I've used in case you really want to try something someone else has used, but your sauce will likely require lots of experimentation for your personal preferred taste.
For cheese, you can use mozzarella and provolone slices. You could use grated cheese. Again, it's up to you. For this type of pizza I typically use a grated blend of mozzarella:sharp cheddar:provolone in an approximate 8:1:1 mixture. You could through in some grated parmesan, too.
28 oz. canned tomato puree (Escalon 6-in-1 preferred)
3 oz tomato paste
2 tsp. sugar
1 1/2 tsp. Oregano
1 tsp. fennel seed (whole or ground)
1 tsp. fine basil
1 tsp. chili powder
1/2 tsp. powdered garlic (may substitute with 1 clove of fresh garlic)
1/2 tsp. black pepper
1/4 tsp. cayenne pepper
1/3 tsp. onion powder
1/2 tsp. fine salt (popcorn salt is preferred, or may use salt substitute)
Add water to desired consistency (usually about 4-6 oz.).
Stir thoroughly to distribute seasonings
May be used immediately, but better if refrigerated to allow herbs to permeate the sauce.
Use approximately 1/8 to _ cup of sauce for a 14-15” pizza