I've done this a couple of times and come to the conclusion that I'm hopeless at predicting what I will miss and what I will replace. I also had a conversation with my aunt where we both laughed 'til we cried about putting stuff in storage and then realising that we weren't using the stuff we'd kept out of storage and were buying seconds of things that were in storage.
I moved stuff from Aus to the UK for less than the prices you are talking about, and there seemed to be even more shipping options for NZ. Not sure if the same applies for moves to the US.
Things I miss (my stuff is currently spread across 3 continents):
- kitchen equipment including baking pans and tools that I used regularly (harder and more expensive to replace than I anticipated)
- a few books
Things I have with me that I am glad I have with me:
- wool products from Australia and NZ (doonas, icebreaker stuff, thermals)
- goretex boots, RM Williams
- jeans
- road bike
- mountain bike
- biking accessories (shoes, helmet, tools, cleaning equip)
Things I have replaced that I'm not upset about having paid for:
- running shoes, work shoes
- work clothes that were getting a bit dated
Things I have with me that I regret paying all that money to ship
- masses of clothes
- stereo
- stuff that I hoped I would one day use but actually I'm just not that motivated (hard to read books, clothes that require effort - like, can't wear jeans with them!)
I'm not paying for storage either. My suggestion would be suitcases plus shipping household items you use on a weekly basis; I'd also look into keeping the electricals and using transformers - more than anything I miss the quality of electronics in Aus: super cheap (proximity to Asia?), excellent quality, and a great range. I do also think it's worth considering how much time you want to spend replacing stuff. I got so fed up with the trips to the outer burbs to big box stores for household goods etc, I realised that I would have been happier paying to have my own stuff delivered to my doorstep.
How soon is the move? If you have a couple of months, I suggest taking an inventory of your stuff and ticking off what you actually use vs what you think you use. Also, look into getting rid of stuff you have that you don't anticipate needing after you return, and think about leaving stuff in the US rather than bringing it back so you're only moving it one way. For things like computers and appliances, if you decide not to take them with you it could be better just to sell them now, rather than store them.