Hi Tom
Firstly, its a big exercise planning a RTW ... Do you know how long you want to be away for?
Take a look at
my post on the Great Escapade i did a few years back for some background info and tips. You'll want to research as much as you can, Milliemoo also did a Great Escapade, i'll try and dig hers out too.
Not sure on the price brackets. Safe hotels - any of the major chains should be fine. Its more about area than hotel i would think. And your destinations are all in pretty developed places.
If you book through an agent you may be able to get a discount from booking all the hotels with a chain, but why limit yourself? Look at all the places you can stay and choose what you would prefer, dependant on location and amenities. LA for example is a huge place, did you want to stay in Beverly Hills or Anaheim or Hollywood for example? There are lots of hostels at all of these places, maybe that would be the route for you? I cant personally advise but im sure someone else can - i saw a hell of a lot of students and backpackers on my travels.
As for money, i had put a few tips in my post that i referenced to earlier, but its all down to the individual. Do you spend a lot of credit/charge cards? Do you use travellers cheques? I just take bills for tips and cabs and use cards for my expenditure, but thats how i travel normally. If you are using cash, i'd save at least a grand, if not more. All depends on how long you'll be away.
You may benefit from going to see a GE specialist, TrvaelBag in London (who i used) have trained agents for these trips who have been on them and can advise you on the destinations and things you'll need to know and plan for, so i'd definately recommend a chat, and they can help you with any concerns you may have and iron out any issues.
Thanks,
Sarah