First thing to learn when first emerging out of a tech cave is never listen to the salesmen at Best Buy or the other electronics stores. They are not advising you in YOUR best interest.
If you buy an "unlocked" phone from a retailer you will pay the full, unsubsidized price for the phone which can mean $600 for a phone that you can get locked and under contract with a cell provider for $50 or less. There is nothing wrong with a locked phone and there is nothing wrong with crossing OS systems. Iphones work on Win computers just as well as they work on Macs. And Android phones work just as well as Macs as they do on any other computer. Most cell providers will unlock their phone for you once you have it for a certain period of time (usually the initial contract period). All it takes is a code and the right sequence of buttons pressed to unlock a cell phone and the carrier will give you that code - for free - once the time period elapses. At that point you could bring the phone to another carrier provided the carrier uses the same system as the phone is - two systems GSM and CDMA. (GSM uses a SIM Card, CDMA does not - you don't need to know this or understand this. Basically, Verizon-Sprint = CDMA everyone else = GSM.)
The Galaxy Note III is a nice phone - pricey but nice. The main feature of the Note phones and tablets is that they have full handwriting recognition with a special pen that comes with the device. You can write on the screen - print or script (even the worst handwriting) - and it will recognize what you write instead of having to use the keyboard. Beyond that, there is not much difference from any other similar level smartphone.
I will not get into the IOS vs Android discussion because you will get as many liking one as liking the other.
I will tell you that I have had several Samsung devices - phones and tablets - and the one consistent thing with Samsung has been when a new update comes out for Android, Samsung's attitude is lots of luck, go get a new phone if you want the update (even devices just a few months old). The Note is a Samsung.
It is hard to say who you can trust when shopping for a phone or a computer - but is certainly is not the salespeople. If you have relative or friend who is tech savvy take him/her along and be guided by their experience.