Well, here's the issue you've got think about: The programs that let you earn many free nights the fastest (such as Priority Club and Choice) are also the ones that tend to have the least dependable upgrades and other in-hotel perks.

Hilton HHonors is one of the best for in-hotel perks with mid-level status (free breakfast worldwide, free internet worldwide) but you earn points slowly and need tons more points in most cities than with Priority Club or Choice.

So if you focus on upgrades, you essentially have to give up a bunch of points. If you focus on points, you essentially have to give up a bunch of upgrades.

Next, I think you picked a bad time for this (August). IMHO, you should focus on whichever program has a good points-earning bonus. Best Western and Choice both have promos that end in about a week, and then they're likely to have a "blackout period" on bonuses, and haven't announced the next bonus yet. Had you asked about this a month or two ago, you could have earned enough nights at Choice through 8 cheapo suburban stays in the US for 4 $$$ nights in Italy after Sep 16 (all Italy properties drop on Sep 16 to 8k points/night).

Best Western's problem is that it's promos tend to be capped at just a few stays, earning just one free night, which then expires in half a year, before you can earn another one. If you're also booking online and using a BW credit card, you earn 13k bonus points in addition to that, but BW is another chain where points are typically earned slowly and redemption rates are high.

Meanwhile, "the world" is a big place. There are no Choice hotels in Spain, luckily there are quite a few Prioirty Club hotels. There are no Priority Club hotels in Norway, luckily there are lots of Choice redemption (not earning!) hotels there, and most only 16k ponts/night (thus 4 cheap suburban Choice stays here earns one of those, during their frequent stay 2 earn 8000 total points promos). I've found places in the world where there's only Choice or BW (several small towns along the fjords in western Norway), only Starwood (inside Iguazu Falls NP in Argentina, also Salta in Argentina), only Wyndham Rewards properties (in other cities in Argentina), etc.

So you need to figure out more about where in the world you want to go. If you stick to only giant capital cities (London, Paris, Rome, Tokyo, etc), it's less of a problem, but if you want to see sights away from those big cities, then each country or even each area of each country may need a different hotel program (to be able to do as many of your stays as possible on points).

I thus collect Hilton HHonors, Priority Club, Choice, Best Western, Wyndham Rewards, and now (because of plans to visit Argentina) Starwood. (I also belong to Marriott but so far only for airline promos.)