A quick review of the 7 clubs per your criteria:
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My only criteria is to pick one which effectively utilizes its resources (too jaded by my A&M sporting fandom) and is occasionally (hopefully soon regularly) challenging for world championships ALA NBA or MLB.
Man City: They certainly fit your criteria, but as others have said you won't get much respect for picking them. It would also be a pretty soulless existence I'd think. Imagine someone deciding today they wanted to follow college football and picking Alabama. Sure they'll win a lot, but....so what?
Arsenal: As said above, very exciting young core right now who almost won the league out of nowhere this year and have the potential to achieve things soon if they keep the core together and add the right pieces. They haven't won the big one in 20 years, and the years where they've even been in contention for it have been rare, but even in the lean years they were good for some FA Cups. So mixed results on utilizing resources but an upward trajectory at the moment. (Disclaimer: I am an Arsenal fan)
Man Utd: At one time the team that utilized its resources so well and won so much that everyone else hates them, even though the glory days were now more than a decade ago. Could be on the way back to contender status, but in terms of return on investment, the last 10 years have been a disaster.
Liverpool: Great historic club. For the last several years they have been second best to Man City (winning in 2020 for the first time in 30 years), although this season was their most disappointing season in a while. The good thing about Liverpool from an ROI perspective is even when they weren't winning the league for a long time, they were regular contenders for and occassional winners for big things, even the Champions League. Plus they have the team entrance to You'll Never Walk Alone, which I think is iconic.
Newcastle: Could be on the way up to rivaling Man City due to recent Saudi investment, but it's too early to tell on how good they are on the ROI. You do have to have Phil Mickelson levels of moral flexibility to jump on this bandwagon though.
Chelsea: For two decades they might have fit your criteria better than anyone, although the investment was from a Russian oligarch who had to sell the team in 2022 due to sanctions for obvious reasons. Now owned by Americans and the past year has been so bad it's monumentally hilarious to everyone else. 12 months of no plan other than throwing money around, without thinking about how the difference assets they are buying fit together. Still have enough money they can never be ruled out long term though, especially if they do identify a plan.
Tottenham: Talk a big game, occassionally go on a really good run, nothing to show for it in the end. At all. The least successful so called "big club" by a large margin.
Overall, I echo the suggestion to watch some games starting in the new season and see which team/story appeals to you. If you want to go beyond the "big" clubs there are some interesting mid-table teams with interesting potential or stories like Brighton, Aston Villa, etc.