Here are some species of mushrooms that are well-suited for growing at home in Arizona, along with their incubation and fruiting times, and level of difficulty for cultivation:

1. Shiitake (Lentinula edodes):
   Incubation time – 14-21 days,
   Fruiting time – 4-6 months,
   Difficulty – moderate.
   Shiitake mushrooms are one of the most popular varieties for home cultivation, and they do well in warm, humid environments.
2. Oyster (Pleurotus spp.):
   Incubation time – 10-14 days,
   Fruiting time – 1-2 months,
   Difficulty – easy to moderate.
   Oyster mushrooms come in a variety of colors and are a great option for beginners because they are easy to cultivate.
3. Lion’s mane (Hericium erinaceus):
   Incubation time – 14-21 days,
   Fruiting time – 4-6 months,
   Difficulty – moderate to difficult.
   Lion’s mane mushrooms have a unique, tooth-like appearance and are prized for their flavor and health benefits.
4. Enoki (Flammulina velutipes):
   Incubation time – 14-21 days,
   Fruiting time – 2-3 months,
   Difficulty – easy.
   Enoki mushrooms have a delicate texture and are often used in soups and salads.
5. King oyster (Pleurotus eryngii):
   Incubation time – 14-21 days,
   Fruiting time – 2-3 months,
   Difficulty – moderate.
   King oyster mushrooms are known for their large size and meaty texture, making them a popular ingredient in vegetarian dishes.

It’s worth noting that the incubation and fruiting times can vary depending on the specific strain of mushroom and the growing conditions. Additionally, while some mushrooms are easier to grow than others, all types of mushrooms require some level of care and attention to ensure successful cultivation.