The answer to your question is... it depends. Some great options are given below.
1. Nokta/Makro Simplex+
Pros: Great value for the money (get the wireless headphones version, you won't be disappointed). There is frankly no other detector on the market that beats it in value. Totally waterproof. Rugged. Deep. Easy to use. Great all around detector.
Cons: Single frequency. This means it won't perform quite as well in salt water and wet sand at the beach. It will be fine in dry sand at the beach and even has a special beach mode that can do some basic salt water hunting. But it is not as good in salty conditions as a multi frequency machine.
2. Minelab Vanquish
Pros: Great value for the money for what you get. But you will pay more for a headphone version than you do for the Simplex. It is multi frequency which means it will work great in pretty much all conditions, even salty wet sand at the beach. Good depth (on par with the Simplex). The multi frequency also helps in mineralized ground conditions and provides more stable target ID.
Cons: Not waterproof so you would not want to take it into a lake or in the surf at the beach. For some people this is not a deal breaker. For all the other cases you mentioned you should be fine. There are three different models of Vanquish with various features. The only one that supports native wireless headphones is the Vanquish 540.
3. Minelab Equinox (600, 800)
Pros: Great all around machines. They are multi frequency, waterproof, and very deep so they will do well everywhere you want to take them. These machines are pretty much what everyone who can afford them wants these days. And I don't blame them.
Cons: Cost. These are pricey for a beginner. But for someone who has been in the hobby a while they are worth the money.
4. Quest X5/X10
Pros: Very inexpensive for a machine with target ID. These are a great value and perform fairly well.
Cons: Single frequency and not waterproof. Also, they do not have wireless headphone capability so if you want that you are going to be buying some additional add on module to get it. Being single frequency, they won't do well in salty conditions/water. But they can be used in dry sand. I would not take them near water.
Other detectors - I think there will be some here who will recommend some other brands of detectors because they have used them and found them to be good machines. Garrett, Fisher, and other companies have some good machines. But I just don't think they compare anymore on a value and feature basis with some of the detectors available today. The Simplex and Quest are fantastic values and the Vanquish and Equinox have you covered on multi-frequency capabilities. If I were buying a machine for someone today, my first question would be cost. If they want something cheap and don't care if it is waterproof, I'd go with the Quest X5,X10. But if they are willing to spend an extra $50-$100 then the Simplex can't be beat. And if they need multi-frequency, I'd steer them toward the Vanquish and Equinox.
Finally... none of these machines are good for small gold flakes. So if your intention when going to Arizona is to gold prospect, these are not the machines to take. They will all work on larger gold nuggets to a certain extent, but your odds of coming across such a nugget while vacationing are quite small. All of these machines are great at the park, fields, fresh water beaches, and dry sand at salt water beaches. Some can handle water detecting and deciding up front what type of detecting is the most important to you will help steer you in the right direction.
These are all just my thoughts and opinions. Others here may agree or disagree.
