For big name players right now? I'd say we're at the cusp of Top 5, as things stand - and maybe historically too if you include peak Milan, Juventus and Internazionale. Real Madrid and Barcelona are definitely ahead of us and every other club. As long as they have money to spare and are successful, we (and every other club for that matter) don't stand a chance to compete (especially for Iberian and Latin American footballers) because top footballers are both basic and obscenely rich. A millionaire from those parts would rather move to those clubs for cultural, historical and lifestyle reasons - or the chance to play with the likes of Messi, Neymar, Ronaldo and co. PSG are in the second tier because of their shrewd recruiting process in recent years, and their contingent of Latin American players, plus Paris has a reputation for being a glamorous city for people with money, so there's that. Bayern Munich too because of all the success they've had recently (though they're not likely to sign many big name players so it might be a moot point). Outside of those four - Chelsea might have the London factor in the favor and City can spend loadsa money, so they might pip us for a few players; but if push comes to shove, we can compete with either because Woodward has already thrown caution to the wind. If we were successful like in the Fergie days, I'd say we're neck to neck with Bayern Munich, or maybe even ahead of them because of the lure of the Premier League, which is more marketable than the Bundesliga. Plus, English is a universal language as opposed to German when conversing with the natives. However, Bayern has one key factor working in their favor - that's proximity to a reservoir of relatively cheap talent - they can sign a lot of German and Bundesliga based players before anyone else gets a whiff, which gives them an advantage because they're cheaper compared with their Premier League counterparts.
Considering all of that, it would make sense to target players right on the edge of greatness, rather than the finished product - because if a player achieves world class status with us, he might be more emotionally invested in the team, as opposed to a hired gun who has become jaded over the years and is a strict 'pro'; or in the case of ex-Madrid, Barcelona players - maybe surplus to demands, and not operating with optimal mental acuity because his head is still there. That's not a universal rule, just an anecdote. With that in mind, we should seek to emulate the Atletico model (or our own old model for that matter). They signed Falcao when he was on the threshold, even Griezmann, Godin was a retread - and have built a system where they can add 3-4 good but not great players every season like a conveyor belt without a lot of attrition in terms of quality, including youngsters like Vietto, Correa, Giménez. That's what Fergie did over the years - signing Ruud, Cole, Stam before they exploded, on top of Ronaldo, Rooney and it served us well. And unlike Atletico, we can afford to retain most of our stars from a financial perspective. However, they have the advantage of having probably the best crop of homegrown players in Europe with the likes of Koke, Saúl, Óliver to form the bedrock for the future - and you don't see that type of quality in our youngsters. Also, by and large - Spanish youngsters are much cheaper than English youngsters so they don't have to spend as much. We're suffering in comparison with top Spanish clubs because not only do they have the Latin/ Iberian advantage in their favor; the talent is more abundant and cheap, and they can acclimatize easily to the La Liga. Top English players are both rarer and obscenely expensive unless you unearth gems like Alli from MK Dons, or Stones from Bunrley; or sign them at a very young age before they become proper Premier League starters in an era where teams are demanding £30 million for every half decent player.
PS: Juventus has a great recruiting model too, that's something we might wanna look into. They built a great team without a lot of ready made star quality by pouncing on the likes of Vidal, Bonnucci, Pogba, Tevez at the right time.