Banking in the USA
This happens to be exactly what I do in the real world . . .
Bank accounts in the USA now need to be opened in person with positive ID - just show your passport and give them $100 - you've got a brand new USD bank account with checks and a debit card. If they give you a toaster, ask for something else since the toaster will be 110 volts and won't work when you take it home.
You can bring absolutely as much cash as you want into the USA, but if it is over $10,000, you do have to declare it, expect to answer where you got it, what's it for, etc.
Best solution is to open the USA account when you get here and then wire the funds from home (have someone do it for you) - one of my businesses happens to be currency conversion, contact me privately OFF LIST if you need details.
You'll get hammered if you use your credit card denominated in Sterling or Euros - the exhange rate on plastic is poor.
HSBC has some branches in South Florida, they are not real savvy because they are essentially local banks owned by HSBC in London. The brains are in London, the tellers in S. Fla have few clues and this is NOT really an international bank, just one that is owned overseas.
No Wells Fargo in Florida, Chase will be happy to help you if you are talking $500K or more - they don't like us poverty-stricken aviators very much.
I've been doing this (international banking) for almost 15 years, most of my business is back and forth with the UK - if the moderators have no objections I will answer questions here (it IS of benefit and aviation related), if they do object, please contact me privately.
Best Regards,
Echo Mike