Is there possibly a shop where I can sell materials and food for a higher price than regular merchants like Beetle? Or do they all offer the same prices?
There is no shop per-say, but there are people that will buy your things for more money. This is not an exhaustive list, but any means, but some examples are...
Fireproof Lizards can be sold to a guy in the mines to the south of Goron City. He'll first give you an item, and then will buy three lizards at a double-cost rate to what you sell them for to merchants.
There's a guy in one of the stables that will buy your Gourmet Meat at 100 a pop, though you can only sell to him a few times a day.
There is a Gerudo who walks around the Goron town. She buys gems at a rate higher than a shop, in chunks of 10 at a time. If you have a fair amount of gems, she's a great npc to visit.
I know of two other NPCs that will trade items for rupees.
- In Rito Village, there is a lady who will buy baked apples from you. The more baked apples you give her, the more rupees you get per apple. Apples are fairly common, and you can bake up to 10 at a time if you have access to Death Mountain.
- In the stable just before the entrance to the Gerudo Desert, there is a man who will buy 55 Rushrooms from you for 330 rupees (by comparison, most merchants pay 165 for the same amount).
I don't think this one has been mentioned yet, and correct me if it doesnt really fit the OP's questions, but after you complete a certain quest in Zora's Domain, you can trade 10 Luminous Stone's to a guy for 1 diamond which sells for 500. Luminous Stone's only sell for 30 each so that's a pretty good deal. And its something that can be repeated endlessly, as long as you can find a good supply of stones.