First off, it's good that you already drive a manual, as it is slightly more common in the UK, and if you take your UK driving test in a manual, you can drive both those and automatics, whereas if you take your test in an automatic, you are qualified to drive only those.
There are not many changes you can make to help ease the transition -- unless you have some nice quiet road in the middle of nowhere upon which to try the "other" side of the road!
But in order to pass the UK test, I would say it's always handy to start really strictly abiding by all those things we all let slip over the years -- strict "mirror-signal-maneuver" protocol, always signalling correctly when needed, doing your three point turns and paralel parking with greater care than we mostly fall into bad habits with....this kind of thing. I think for me, my bad habits are what are a challenge to get rid of now. They are the kinds of things that haven't caused accidents, death, maiming and bodywork, in other words things that don't seem that serious to do half-assed or not very perfectly, but which would bring you closer to a fail score in the UK test.
So I would say, get your DSA stuff definitely, get the UK Highway code and start learning some of the road signs, road markings and laws/rules/regulations that happen to be different from the US ones (some are the same or similar).
And work on doing all your manoevers, signalling, lane changes, etc the way students are originally taught instead of the "bad habit" way.
Another thing is crossing hands when turning the steering wheel -- it won't necessarily get you a fail on the UK test, but it's kind of more frowned upon in British driving than it is in the US. Here it's recommended more to "feed" the wheel through hands kept in the 10 and 2 oclock position. I've been trying to do that but it feels more awkward to me than a good honest crossing of hands.
One thing I feel though, is that if I were you, I would NOT plan on driving myself from the airport, "straight out of the gate" so to speak.
Before I came to the UK I thought tha driving would be fine once I got behind the wheel, because I was an experienced driver in the US.
But when I did first get behind a wheel, I was deeply shocked at how badly it went and how frreaked out I was.
Others may be fine, but I've more often heard of people from the US being the way I was; even grown men who thought they would be just fine, it's only switching sides of the road, isn't it? (!) No, it feels a lot more challenging than just that. So please don't underestimate how little prepared you might be to drive straight away. Don't want to make it seem impossible -- like I say, there must be people to whom it all came very easily, but I hear more often that if people are being honest, it was harder at first than that.
So, maybe leave out the plan to drive right away straight from the airport, but definitely go ahead with buying some DSA packs, learn your UK highway code, and brush up on all the "technique" stuff that they are strict about on the test but that we all let slip in our daily habits. Good luck; I'm taking my test soon and I haven't had a whole lot of prep or help.
You're doing great getting a head start.