UK:
The key to the UK opening is making the best use of your limited number of transports. Any transports in the Atlantic that survive the German opening attack are still far enough northwest that they’re stuck in the northwest – at most, they can make it to Gibraltar or Morocco. You don’t normally need to take Normandy or Gibraltar on turn 1, so what you do with your Atlantic transports is usually not very important – the smart thing to do is to either stack them up with what’s left of the British Home Fleet (if that’s enough to keep them safe) or send them fleeing west to Canada to be part of a rebuilt British Home Fleet (if you’ve taken heavy losses and need a couple of turns to rebuild).
Outside of the Atlantic, you should have exactly two transports: one near Egypt, and one near India. You have several plausible targets for these transports: Southern France, Greece, Tobruk, Ethiopia, Persia, and Sumatra.
First, the niche cases. Southern France only makes sense if you’re playing Balanced Mod (to stop France from selling out ala Vichy) or if for some reason it’s clear that Germany has committed 100% to an Afrika Korps strategy and you need to shut down the German Med factory.
Likewise, Greece only makes sense if Germany is severely over-extended – if both Germany and Japan declare war on turn 1, or if the Axis have declared war (or are clearly about to declare war) on the true neutrals. Greece makes a great monkey wrench if the Axis are relying on split-second timing to get their troops where they need to go, but you’ll lose your transport and you’re not actually going to kill many enemy troops or earn much income with your tiny Greek army of six units (four neutrals plus your one loaded transport), so don’t go to Greece without a good reason.
The strongest play, in my opinion, if you can get away with it, is to send your transports to Persia and Sumatra. This activates the Persian infantry so that they’ll be ready to attack Iraq on UK2, activates the Persian territory so that you’ll be ready to build a factory there (and send the Russian mech on its merry way), and jacks up the UK Pacific income to a safer level. Yes, Japan can crush you in Sumatra – but they only have so many transports, so they can’t take Hong Kong and Malaya and Borneo and Sumatra and the Philippines all on one early wave of attacks. Holding Sumatra means you’ll still have some respectable income even after one round of Japanese attacks. I say “if you can get away with it” because sending a transport to Sumatra is much less justifiable when Japan has already declared war on you – you’ll lose the transport faster and you won’t collect the extra income for enough turns to pay for it.
If you can’t or won’t go to Sumatra, another option is to send both transports to Ethiopia, along with the mech and tac bomber from Egypt. People often send one transport to Ethiopia, but I think that’s a mistake – Ethiopia is not a critical territory, and with only one transport, you’re not getting great odds – so why use a scarce resource (your transport) to set up an optional battle at only moderately good odds? The point of going to Ethiopia is to wipe the Italians off the face of East Africa, so that your existing units in the region can easily mop them up next turn, and your transports and aircraft can start moving elsewhere. If you’re going to have to transport units to Ethiopia again on UK2, there’s not much point in going there at all on UK1. In the long run, those Italian units have nowhere to go; they’re surrounded by British and French on all sides and they have no navy and no factories.
Finally, there’s Tobruk. Only one transport can reach Tobruk, but you can get a fair amount of air power there, and you’ve got your land stack in Alexandria to fight with as well. A lot of people like Tobruk. I’m not one of them; I figure that Italian units are much better placed in the worthless deserts of Africa than as can-openers in the fertile Ukraine or as a pain in my rear soaking up the oil of the Middle East. If Italy wants to send reinforcements to Tobruk, that suits me just fine – if UK instead uses its air power to knock out most of the Italian navy at Taranto, then the Italians are never going to take Egypt anyway, let alone penetrate to Iraq. That’s also part of why I like to go to Persia early – if you build a factory there on turn 2, then it’s a flexible source of reinforcements that can go west to Egypt, east to India, or north to the Caucasus as needed.
For those of you just tuning in, the Taranto raid is an attack on SZ 97 (the east coast of Italy) on the UK’s first turn. Different people recommend different configurations of units, but I like to bring in the entire British Mediterranean fleet minus one destroyer, plus every British plane that can reach. Note that planes in London can usually reach; some of them can land on the carrier, and the planes that started on the carrier can land on Malta, where they’ll be reasonably safe because they’re protected by an infantry and an AAA gun. I then also attack SZ 96 (Malta) with the Mediterranean destroyer and the cruiser from the west coast of Gibraltar. If that cruiser died to a German sub attack, I replace it with a single fighter. When the dust clears, Italy should be left with only one fleet and only one transport (in SZ 95, the west coast of Italy), and they just can’t do much damage with it, nor can they afford to build more – with only 10 starting IPCs, the best Italy can manage is either a transport or a destroyer, neither of which is likely to allow them to survive a follow up attack by all of the planes you landed in the Mediterranean. If the Germans invest very heavily in the Med by sending the entire Luftwaffe to crush the British navy there, the Italians might manage to eke out a marginal victory and keep a boat in the water…but then Russia will have a much easier time holding its southern flank, and your factory in Persia can send forces west to hold Egypt.
No British opening guide is complete without a few words on whether to scramble your planes to defend the British Home Fleet against a German air attack on turn 1 – and my answer is, yes, scramble if Germany tries to attack both of the major UK fleets (SZ 111 and SZ 110). Statistically, you expect to lose money on that battle, and you might get wiped out quite badly, but you can afford to replace your planes, and Germany can’t. A big win for Germany over the skies outside London means that Italy gets off to a slightly more powerful start while still ultimately being contained; a big loss for Germany over the skies outside London means that Germany is toast. You can also scramble if Germany does something weird that makes the German planes vulnerable, like attacking four different smaller fleets, or sending only five planes to attack one large fleet while using the other planes on land. The only time I wouldn’t scramble is when Germany concentrates its planes against one large British fleet – if you’re going to be outnumbered 10 to 6, then it’s not worth throwing your planes away.
In terms of what to build, I’m a fanatical advocate for 2 infantry, 1 fighter in London – it’s enough defense for London that if Germany tries to do a Sea Lion, he’ll wish he hadn’t. Germany might wind up taking London, but not at a price he can afford. Any more defense of London is overkill; any less is too risky. I think you also need to build at least 3 land units in India, so that you don’t wind up giving India away to Japan too cheaply. Other than that, pretty much any purchase can be made to work out – you can spend the remaining money on a destroyer to fight for the Atlantic, on a transport near South Africa to get more efficiency and flexibility in the western Indian Ocean, on mechs and tanks for India to help it stack Yunnan, on artillery for India to help it trade Burma deep into the middlegame, on an additional plane, or even on a first-turn minor factory in Egypt if you’re doing a full Taranto attack. You can even get away with saving the extra money – you’re not likely to run out of build slots, and you may have a better idea of where to spend the money one turn later.
Finally, I’m not reprinting it here because this is meant as a ‘beginner’ guide to Global 1940 openings, but check out @crockett36’s radical new ideas about Operation Richochet in the UK Middle Earth thread – he suggests that the key to victory as the UK might be not to attack anywhere at all, but instead to conserve and position your forces for a glorious comeback on turn 3 or 4.