I've done that, only I went the other way round - this is because the jet lag is slightly less painful if you go westabout, although the flights are longer.
How much money is 'how long is the piece of string' but here are some thoughts:
1) Aussie and Kiwi dollars are currently very strong against the pound (what isn't). Oz in particular at 1.6AUD to the pound will be really pricey for you. Hostels begin at $30 a night and most of them aren't very good, shop around on hostelworld and read reviews as there are some nasty spots. Remember the obvious size of Oz and don't try and do too much.
2) New Zealand has an excellent hostel network and now about $2 to the pound, dorms from $25 and doubles from $60 for the room. The usual mistake is not to allocate enough time to NZ which has loads to see and slow roads; minimum 3 weeks for one island only, 2 months for both islands. Or visit five times and spend four months at a go like I have, and still not see everything!
3) SE Asia is a lot cheaper - Singapore is fantastic, Malaysia lots of great sights and wonderful food , Thailand pricier but still lots to see and huge. This needs a lot of research and the more exotic spots such as Cambodia, Laos and Vietnam (and indeed some parts of Malaysia) need malaria propylaxis. Everywhere needs 50% deet all the time against dengue.
4) Hawaii - you land on Oahu, visit Diamond Head, go to Waikiki beach, think 'tenerife is better', visit Pearl Harbour and maybe the north shore. I would recommend Big Island for the volcano park but again research is needed to get good car hire etc (no public transport except on Oahu). Due to its isolation Hawaii is VERY expensive outside Honolulu. Again, look on hostelworld.
5) LA is good but San Francisco is better if you haven't been there.
remember of course travel insurance for all these places. To make the most of this trip you need around six months depending on how much of Oz and NZ you want to see.