I don't think there is an answer to this. Neither we nor you know about what the next travel location is. So, you cannot prepare for it. Even if you stock up on some books (or anything), you may need to travel 100 or 10 000 times before whatever you stocked up on would have any worth. And 100 or 10 000 hops may even land you in something that's not worth ruling over. Maybe there is no more France. Not as a country but as geographical location. You can very well go into a reality where humans don't exist. Or maybe you succeed - there is no definite way to know.

The plot takes care of the odds, so I've chosen to dwell on the "maybe you succeed" part and not "in reality, this is probably a bad idea" :). The point of the question is finding the circumstances that give the best chances, not why it would fail most of the time (which I'm fully aware of).

"But I don't care how terrible the world become as long as I can rule a decent part of it (at least a country)." Progress until war and plague has killed everyone else on Earth, now you rule the whole world.

If everybody travels to a worse reality at the same time, where does it go the one in the worst of them?

Or to continue @Chococroc's line of thinking: What happens in the "best" reality, since there was no you to fill in the gap you left behind?

Could you transport everyone else to the next reality? Does it count to rule the world if its empty of people?

Plot twist: you aren't actually jumping realities, merely changing history.

There are other questions to think about. Who is pushing or pulling your alters? If every alters must travel at the same time what will be their motivation for this? If one of alters will find the world to achieve their goal will others be stack in not-so-good worlds? What if one of alters IS a leader of a country?

@Chococroc & @ LHM there are infinitely better and infinitely worse realities. Probably. @ Amy no, unless I can convince everyone to come through my mysterious door. @ user253751 maybe, who knows? @ mr4eshir good question, maybe the universe, or what created the door in the first pace, tries to balance itself to the best of its capacity: if I shove someone through, their predecessor could very well just stumble into it by accident.

How do you define the axis of these upcoming worlds? It's this property even transitive, or is the "worst" for you 100 hops ahead is your "better" one? If you say, there are infinite number of worlds on this axis, it means that countable number of jumps wont' bring you to a reality which is somehow visibly worse.

@Askar Kalykov It's possibly infinite, but there's no way our protagonist can know that without travelling as far as he can

@Chococroc It is badness all the way down!

Troll Answer : ~~Florida~~ France man keeps reality hopping to worse realities, arrives to an irradiated molten sea and dies

It's a shame you specified becoming a dictator in your own lifetime. Another variant of this theme would be someone who becomes a saint/messiah by travelling to a worse reality and preaching all the goodness of their own reality. They might get killed for it by the bastards of our reality, but their name might still live for millennia.

Dictators tend to come into power by leveraging public fear or mistrust, so... going to worse and worse realities would only be increasing your chances, would it not?

What if you go to a reality so bad that humans don't exist at all and there is no such thing to call as France in a meaningful way?

What if you go to a reality where Germany won WWII and there is no France anymore? What if you end in a reality where France lost the Hundred Years' War and now is part of England? Or to a reality where the Kingdom of the Franks was sucessfully conquered by the moor invaders in Dark Ages and is no more than a small note in history books about a short-lived barbaric kingdom that ceased to exist more than a thousand of years ago? Or to reality where the Attila lived a long life as a cruel emperor, having won the Battle of the Catalaunian Plains and there was no kingdom of Franks at all?

What happens if you died in the universe you're going into? Or the one better than yours? What happens if you turn on your garden house and take it through the door? Or your Ethernet cable?

@VLAZ, if all versions of traveler jump at the same time, the initiator can make suggestions for his replacement, and before too many jumps, all versions will figure out what’s happening and leave clues. Unfortunately, you don’t see the clues till after you jump, so there’s no way to decide what best to bring.

@WGroleau exactly. At best the clue could just describe what's different in this reality, e.g., "Goete was never born". But you cannot really use this information until after you arrive. No way to prepare for it only react.

@Victor Stafusa see my second comment

"Let's say I'm a normal person, in my thirties, having the ability to travel to alternate realities." "normal" 🤣

This isn't really the plot to Candide, but somehow this feels like Candide. I predict your protagonist becomes dictator, learns how to travel home out of love, realizes they should have just stayed dictator, and ultimately comes to the conclusion that they keep #$%^ing up and should just buy a farm and settle down