This was fun as hell now that I could actually do something, so a lot of things have changed since my first post on this.
Here's how far I've gotten (the green area to the right of British India is Burma, which is my puppet, so that's mine too). The year is 1875, and I've done just about everything I said I would do. The Phillipines are mine, most of Indonesia is mine, just about all of the small Oceanian islands are mine. I was unfortunately completely blocked off from Africa by Austria quickly nabbing Somaliland, so that front is closed for me. I have also allied myself to the US, so I'm not going to invade there. Still have the rest of Indonesia and Siam, though, which are both easy targets. The Chinese Empire has now been reduced to pretty much a joke, as I am so advanced that the Chinese numbers no longer matter, so I can pretty much grab land at will there. Then there's Arabia as you said. But I decided on something a little less obvious: South America. Just before I quit the game for today, I declared war against Colombia in order to grab Panama. Then I'm planning on chomping up the western South American coast before munching up as much of the continent as I can.
I have also decided to stay on good terms with Britain, as I discovered that I still wouldn't stand much of a chance against their fleet.
Ah, well good luck with that, the problem with the British fleet is just that it is too large to take on in a fight, but I've learned that it's possible to blockade the Suez canal with ground troops, it is possible to end a war before their fleets arrive from sailing around Africa, but it's very hard and you need a lot of luck to do it.
This reminds me of my latest game of HoI 3, here's the map at the end of the game:
Unsurprisingly I played as the Dutch, I modified my game a little at the start to give me claims to Belgium and Luxembourg and got rid of the UK and France guaranties on these countries.
A month of war later they both surrendered to me, the only thing I didn't take was the Belgium colonies in Congo because there was no way I could protect them.
After that I started to build up my Naval strength, aligned myself to the Axis and started to research the Atomic bomb techs, the invasion of France was hard on me and French troops temporarily managed to take a few southern provinces while I tried to defend my coastal provinces from wave after wave of British naval landings. But it didn't take long for Germany to break through the French defensive lines and after my air-force sank two British Battleship, one Carrier and some smaller ships they also backed off.
With the fall of France I could focus my attention at the east indies, my fleet that consisted of one battleship two light carriers, two battlecruisers, about 20 lighter ships and 10 transports had already moved there when war was about to break out.
My first real victory was the puppeting of Malaya and the capture of Singapore, the large British fleet that was stationed at Singapore had been harassed by my air-force for months (It took a long time to capture the heavily defended port). When they were forced out of Singapore by my victorious infantry the fleet was barely holding together, around 6 naval battles took place in the following weeks as my fleet followed the British retreat, they lost large amounts of ships including some battleships and battlecruisers, I only lost 3 lighter ships.
I forced the Brits out of Ceylon (Sri Lanka) and took their islands in the Indian Ocean. Meanwhile the Italian campaign in Africa went surprisingly well and China had become a Japanese puppet.
The Brits kept trying to force naval landings in the Netherlands itself but I managed to defend myself quite well, it's also important to know that they didn't once try it in German occupied France, this is important later because Germany could Focus all it's attention at the Soviet Union when war broke out with it.
I attempted multiple times to make Australia a puppet of mine but they had a surprisingly large army available to defend their continent, when the war with the SU began I decided to put expansion in Asia on hold and took my fleet to the Suez (Capturing a few ports in Arabia along the way), I managed to land in the Suez just before the Italians took it, after that I took Crete and Cyprus before landing my troops in the Crimea (The Germans had already pushed that far by the time I arrived). I pretty much obliterated the Russian Black sea fleet and only took minor casualties while doing so, but to late I realized my mistake. Australian troops had made landings all over Indonesia, I doubled back and pushed them out with little trouble and realized I had to defeat them, luckily I just finished my first Atomic bomb. During the Australian campaign I dropped three of them in total and I started to push back the demoralized armies. I din't take long before the became a puppet of mine.
Germany made peace with the SU and gained massive amounts of land, I invaded the rest of Arabia just for the hell of it and made New zealand a puppet. while I was fighting there German boots landed on the British islands. I made my way to Gibraltar as soon as new zealand surrendered and took it after a short fight, than I landed in Southern England, I could have taken Londed but decided not to because I wouldn't get the events to dismantle the British while the Germans would if they took it.
England and Scotland became German puppets, I kept southern England and the US became leader of the defeated Allies.
To my surprise the SU had recovered and had made Persia, Afghanistan and Pakistan Puppets and was pushing into independent India just like Japan, I decided to join the party.
New zealand declared its independence from me but I had already deployed my troops in Greece, the Italian had failed to break through their defensive lines and were too stupid to make a landing in their capital. Two atomic bombs and a few landings later they surrendered to me.
Unfortunately the Yanks had pushed the Japanese back so I decided that New zealand could wait, I had to fight the United States. The game Ended during my fourth attempt to storm Guadalcanal with the whole of my east indies army, I wasn't winning.
In the end I had the fourth largest navy in the game, I was the only nation capable of using atomic weapons and we were on the verge of another war with the Soviet Union, all in all a successful game.