Transit in the US, I have to admit from time to time is not entirely painless. However, I do recognise more out of the first description than the second.
So long as you have filled out the required forms, either en-route or on-line prior to flight in accordance with the fairly clear instructions on each, then the worst part is normally queueing up to pass through immigration. Just remember that all customs and immigration folks worldwide have a sense of humour bypass as soon as they get the job. However the yanks have done a fair bit of customer service work with their front line folks and they are probably about the most courteous border personnel you will meet outside of select Asian countries.
Once through, pick up your hold luggage, even if it has been booked through, pass through customs, handing over your customs form, head out to the transfer area & hand over your hold luggage again, assuming it has been tagged through to your final destination. Back to departure security & head airside.
This is the bit which really pisses me off, after having flown across the atlantic, I do think that it's a major "slap in the puss" [to use a fine old scottish phrase] to the traveller to have` to go landside & pass back through security. Fair enough if you're arriving from a country where security scanning is marginal then to send these passengers landside to re-scan them at security is probably fair enough, but sending passengers round from a location where scanning is fairly comprehensive round through security again just aggravates tired passengers leading to air rage unecessarily.
Apart from that gripe, my advice to you is to save your £300 as it'll pay for a whole lot more relaxation than you should accumulate by transiting the US.