Flying around the world, from the standpoint of the flying, is actually quite boring. You have to cross vast areas of nothing. Then there are vast areas of administrative hell. Few things you need to consider, Crossing the Atlantic, you can't get insurance unless you have done it before with somebody qualified. It is also super , super boring, get several books on tape. You need to have your aircraft and your survival equipment inspected and cleared by Canada before the crossing, assuming your starting in that direction. You then need to ensure your radios meet European spec channel spacing. Get used to taking a pile of paper with you into flight planning at every stop. It will usually take far longer than you can rationally expect at every stop. Things like O2 and piston oil will be unavailable, Avgas needs to be arranged beforehand in much of Africa and try not to be shocked at the price. You can wait 8 hours trying to get a low altitude slot to cross the channel to Europe from England. There is no longer any Avgas available in most of the Pacific, you will need to ship it ahead of time. Don't even think of flying across India and Pakistan, you can't carry enough paper and bribe money.
You have a place you want to fly, dismantle your aircraft and put it in a container. Re-assemble it and fly around Australia for example. My 206H Amphib I bought in India is arriving next week in a box, big party to un-box it and get it all in the hanger. I don't mid flying nearly anyplace, but I have been flying smallish aircraft internationally for decades now. It takes a bit of pre-planning, and some gear, but do it in a turbine aircraft, pistons have the big swaths of Avgas not available problem. I once bought a Caravan in Venezuela and flew it to Somalia in 4 days, no preplan on that one, just had to wing it. 72 hours of flying in 96. Still had issues in Canada about new equipment requirements they kind of made up on the spot. France was delightful and denied entry to one of us. We couldn't get clearance to cross the channel for a day and none of Europe has O2.
That flight was a pain, since I didn't have time to tank the aircraft and had to hop about with internals. When you tank it, you can hop over the areas populated by bureaucratic pinheads. That can be hard to do with smaller piston aircraft. They seem to crave a bit of oil, so 12 hours can bring your oil level down to damaging levels at altitude. You also will need an HF radio, they are big, expensive, heavy and über un-reliable. Flying around the world is a nice romantic dream, but it is mostly boring, a paperwork nightmare, expensive insurance and an avgas and oil bill that will choke a moose. Fuel in the 90's to do that Caravan flight, $15,500 one way. Fuel today, same route distance for a Caravan I just bought, $50,500. So win that lottery and have at it. Have Global do your clearances and start shipping fuel in barrels now.