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If you've applied for a passport in 2016, you'll already receive a biometric passport, so you do not need to be concerned about that. This will be evidenced by the symbol at the bottom of the front cover.
Source: gov.uk
After you get your passport, you can apply for the ESTA. Be sure you only go to the official ESTA web site as there are fake ESTA web sites around. You should be charged exactly $14 USD; if you see a larger number than this, you are on a third party web site.
You don't need to worry about APIS. This is handled by your airline. After you book your tickets, the airline will submit your details to the US to verify your clearance to enter the country. This happens behind the scenes and as long as you've given the airline your correct passport number, and your ESTA is approved, it should go fine.
As for how much money you need, you only need to:
Make sure you have enough money to afford your holiday.
This amount will vary depending on what you plan to do. But you will need to pay for accommodations, food, travel, tourist attractions, souvenirs.
When the CBP officer asks how much money you have, state both how much cash you have on hand, and how much you have access to in your bank accounts.
The CBP officer will not be looking for a specific amount of money. Rather, he will be looking to find out whether you have actually put thought into how much money you need. You should be able to describe your plans and the expenses you expect. A printout of your current bank balance can be helpful as you might be asked to prove that you have access to the money.
As for cash, you don't need to bring any cash, as long as you have debit or credit cards that work in the US. Contact your bank(s) before you leave the UK to advise them of your holiday and ensure that your cards will work in the US. However, you should obtain some cash, because while plastic is almost universally accepted in the US, foreign credit cards don't work in a few (largely unpredictable) places. Also, don't be surprised when you insert your card into a chip reader and are told that the reader doesn't work and to swipe the magnetic stripe instead.
Make sure you have return air tickets.
Finally, on your first visit to the US, you must see an immigration officer, then after you're cleared, claim your baggage, and see a customs officer. On future visits you can use Automated Passport Control kiosks for immigration clearance and go directly to baggage claim and customs.