You can buy a basic pay-as-you-go Nokia or Samsung phone for £10 to £20 ($15 to $30) from phone shops & the larger stores of grocery retailers such as ASDA (owned by Walmart) & Tesco. These always include texting, memory, messaging, clock, etc, even basic games. Cheaper if bought on-line but I doubt the complications worthwhile for a visitor, simplest to buy when you arrive though the choice will be more limited. Even at that price, some come ready-loaded with £5 or £10 of air-time.
Here's a couple of examples
You can top-up airtime at most newsagents shops, supermarkets, motorway service areas etc - normally p-a-y-g phones come with a card (like a credit card) which is swiped when you top-up, avoiding the grief of tapping long transaction numbers into the phone. Very easy. The minimum top-up is £10 or less. At any time you can dial up a recorded voice telling you how much credit you have left.
Wide range of airtime suppliers, each with their complicated pros & cons. Cheap phones are usually subsidised by an airtime supplier so you'll probably not be given a choice of airtime supplier, but in any case it'd take days to work out which is best so just go for the cheapest with a mainstream airtime supplier.
Two other thoughts.
Bring your own phone - pay-as-you-go sim-cards are available for about £5, mebbe they fit your phone.
We've just returned from 3 weeks in the US. We'd planned to do the same as you but didn't follow it through. We found & booked motels a day or two ahead by I-pad, with modern booking systems it's so much easier than phoning or texting.