I think its a smart thing to find a hotel after a long flight from the UK, and unwind a bit after a long flight. This should also help you readjust a bit from jetlag. There are a number of large name-brand hotels on Century Blvd next to the entrance to LAX (LA International Airport) -- Radisson, Hyatt, Sheraton, Crowne Plaza, Mariott, Hilton, Westin, Renaisance, Embassy Suites, etc. Those are probably the easiest -- and I'd bet all of them have a shuttle bus to and from the airport.

However, while in general these hotels are large with the usual large hotel amenities, these hotels are a fair distance from the beaches or major shopping areas. Mass transit in LA is OK -- but not wonderful. The Metro does not really go near LAX, other than one terminal on Nash Street, south of the runways at LAX. LA is big in scale -- something like 5x the area of greater London, so while there are buses, the subway/ light rail system only covers a few routes. My recommendation would to either a) Stay a hotel near LAX just to recover, or b) Take a taxi closer to where you want to visit, and then stay there (there are usually hotels near all major destinations).

Most car rental locations are near the airports, or other major transportation hubs, although there are some scattered about everywhere.

If you're concerned about driving in the US, the 2 or 3 things to keep in mind are:

a) You'll be driving on the other side of the road, compared to the UK. So be a bit careful starting out, since as a force of habit you'll be looking the other way for oncoming traffic. (I know, I do the same when I'm in the UK -- including stepping off curbs at street crossings!!)

b) Like any big city, LA has "rush hour" traffic, when traffic ebbs and flows into the business districts of the city, and then back out in the evenings. The downtown area and LAX are a couple of business hubs that traffic flows to and from. So you might consider getting a little bit of late start (say hit the road about 9 am or so) on your first day, to avoid the folks heading to work.

c) In general, LA (like most of the US) has very good signage for roads and highways. A good paper map, and perhaps some printed directions should do you fine. However, these signage are different than what you are used to. the Interstates are typically large freeways (up to 4-5 lanes on each side) and traffic moves pretty well, even at rush hour. To speed you along, many freeways in LA have "Diamond Lanes" or "HOV Lanes" (High Occupancy Vehicle), or "Carpool Lanes". These are on the inside of the freeway and limited to cars with 2 or more passengers in them (unless you are in a designated electric or hybrid vehicle). Even in the worst of rush hour, these will move rapidly -- 45+ mph even with stop and go traffic on the rest of the road. However they are limited access -- you can only enter, or exit the carpool lane at designated spots, indicated by a dashed set of lines on the road. Otherwise the marking is usually a double set of double yellow lines which are treated as a physical barrier -- with significant fines if you cross over them (typically $350+ per ticket).

If you're concerned about traffic, pick up your car, have your spouse handle navigation and act as a second lookout while you get used to the driving on the other side of the road, and head for a freeway. The freeway won't give you the challenge of on-coming traffic and should speed you out of the heavier traffic in the urban area, wherever you start from.