Having never been a property owner myself I'm not sure if I can help you with intricacies of tax laws (when it comes to owning property anyway) but most laws will vary state to state and town to town (I think almost all property taxes are paid to the town/city itself the state has little other then help regulate as I understand). You're taxes will also be assessed based on a number of issues from location to near by features/amenities to how nice the dwelling/land is to weather or not you own land in a rural vs urban setting.
To find property simply do a search for US real estate a lot of websites will allow you to search by state, county, town or region.
Real Estate Listing, Homes For Sale and Apartments by USRealEstate.com
^^^ might be a good place to start. Once you narrow it down to a place you'd like to live I'd start searching for local real estate offices and work with an actual agent.
You're going to be hard pressed to find anything in the temperature range you're looking for. Death Valley, California, the hottest place in the US, ranges on average from roughly 45c in the summer to 18c in the winter...but there isn't much going on there. You can however find similar weather/temps around the southwest in places like Southern California, Arizona (Phoenix might be a good city to explore), New Mexico, Nevada (I think) and Western Texas....although it does depend on where you live in those areas as the temperature swings can be extreme from low land deserts to mountains to coastal areas.
If you're looking for a hot climate you'll want to shy away from any northern US state as they usually have mild summers and very cold winters (it does vary by region however). The southeastern US is generally very hot yet extremely humid, the southwestern US tends to be hot and arid.
I'd also think about what kind of culture you enjoy living around as it varies heavily from region to region as do politics, religion, laws, taxes and customs. The southeastern US is going to be starkly different then the northeastern US and both differ from what you might find in the midwest, west coast, southwest..well you get the idea. If you enjoy the culture in Boston you might hate Atlanta, people from New York dislike Los Angeles and vice versa, folks from Texas might feel extremely out of place in Seattle. In other words keep in mind what culture and lifestyle might suit you best as you're looking for a place to purchase, you should find a good fit somewhere but it might limit your options.
Hope some of that was helpful.