Shi is different from a mere "and" because it carries a connotation of "not only".
This is why you often see constructions utilizing both 'shi' and 'sore ni' together, in the following format: "---- shi, sore ni ------"
Technically, this is a way of saying 'and', but it also emphasizes that the first quality listed is not the extent of it.
In English, think of the difference between "The restaurant is cheap and has delicious food", and "Not only is the restaurant cheap, it also has delicious food."
Same meaning conveyed, slightly different connotation.
"Sore ni" in this context roughly translates to "besides that..." and there's no hard and fast rule that says you have to use it or not, but it's generally more seen in situations where the second quality is not something one would directly expect from hearing the first. For instance, "Not only is he good at math, besides that he's also a marathon runner".
Is there a rule or principle about when to use だ in a し、、し、、construction? It seems to overlap with な adjectives. For example: このカメラは軽いし、使い方も簡単だし、それに安いです。 ... but also with temporal nouns as in: すずき先生は、はじめだし、熱心な先生です。 Thoughts about a principle?