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I am curious about what the lowest number seems to be for a Pokémon to be considered an attacker, a defender, a speedster, and so on so forth for each stat.
On that note, for a Pokémon to be considered a mixed attacker or mixed defender, how much of a difference should there be between the physical stats and the special stats assuming that the Pokémon has moves to take advantage of their attacking/defending stats?

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In that case, what are all of the formats? Are they all based around the base stat totals of the various Pokémon?
https://www.smogon.com/dex/sv/formats/ lists all the formats playable for Gen 9 so far. In general, the ones with a decent playerbase are OU, UU, RU, NU, LC, Ubers, Anything Goes, and Doubles. The farther down the tiers you go, the less powerful Pokemon are -- that's the way Smogon's tiering system works. Ubers > OU > UU > RU > NU > PU > ZU > LC is a rough estimate of how powerful a Pokemon is compared to others, but the competitive scene is too complex to be explained that simply. You'd probably get a much better answer from Smogon.

Tl;dr the tiering system basically ranks Pokemon by strength, so lower BSTs are often found in lower tiers (and vice versa).
VGC, Monotype, and every old generation's OU are also popular formats.
Also LC is not technically a tier.
Much appreciated, thank you for your responses.

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You should not think about maximum and minimum stats required for particular roles in competitive Pokemon. Many other factors decide whether a Pokemon is usable in a particular role to where stats give a very narrow perspective.

It is possible to make generalisations such as "wallbreakers should have base 120+", but those are neither insightful (wow! high stats are good!) nor applicable with any consistency. Some outliers:

  • Azumarill has been a relevant wallbreaker and sweeper for several generations despite its base 50 Attack and base 50 Speed. This is because Huge Power increases its Attack to levels that rival Pokemon with base 150 Attack. Azumarill also has coverage for some Pokemon that wall its STABs (Superpower), tools to boost stats (Belly Drum) and ways to overcome its low Speed (Aqua Jet).
  • Nidoking is used strictly as a special wallbreaker, even though its base SpA is only 85 and its base Attack is 102. This is because Nidoking's special movepool makes better use of its excellent ability, Sheer Force, ultimately doing more damage than the best options on its physical side.

From the above you should notice other factors (ex: ability, movepool) that matter greatly in deciding which Pokemon can be considered for particular roles.

Obviously, Nidoking would be better if it had base 150 SpA instead. But even so, base 85 is fit for a purpose in this situation and has seen Nidoking hold UU for over a decade.

Another factor is the metagame, i.e. which other Pokemon are popular and what other options are available. Maybe you won't use Azumarill if there are many Azumarill checks in the format you're playing, or other wallbreakers that outclass it.

You should not think about the difference between a Pokemon's physical/special stats when considering mixed sets, either. What ultimately matters is whether either stat is high enough to be workable. Landorus-T often uses Hidden Power Ice/Fire even though its SpA is 40 points lower than its Attack, but that's okay because its base 105 SpA is fit for a purpose.

From there, you need to consider the metagame: "What Pokemon will this move let me hit that I can't using my main attacking stat? Is that worth it?" Hidden Power helps Landorus-T beat Pokemon like Ferrothorn and opposing Landorus-T that are roadblocks otherwise.

The same story applies to defensive Pokemon. If the stat is high enough to be workable, then we have a look at the metagame and decide what the best investment would be. Often, this simply means capitalising on the Pokemon's strength and maxing the highest stat, but plenty of exceptions exist.

For example, Blissey always maxes its Def (literally because its SpD is so good you don't need to put EVs on it), and the likes of Corviknight and Skarmory are incentivised to run SpD, just because they fight special attackers often.

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