Hi Lavinia! You are going to have to visit NM to try our red and green. They are not anything like bottled hot sauces of the same colors. Green chiles are most similar to poblanos or Anaheim Chiles, but green chile can be killer hot, but even the mild NM green chiles have some heat and a lot of flavor. We normally eat green chile roasted and chopped on food like a vegetable, but it is made into a sauce as well. The red chiles are "ripe" green chiles that are tied up into ristras and hung to dry. If you choose "Red", the chile is a sauce made from the re-hydrated dried red chile pods.
You mentioned home fries. You can get green chile cheese fries out here, and they are wonderful with a green chile cheese burger.