What is your */24 count with Chase? Do you already have any SPG/Marriott cards?
If you are still under 5/24, I would focus on Chase and build out your Chase trifecta, quadfecta, or pentafecta of Freedom, Sapphire, and Ink cards. I would avoid signing up for any of Chase's Marriott cards. The reason is under new restrictions that went into effect on 8/26/18, getting any of the Marriott cards now would, generally speaking, disqualify you from the Amex SPG cards for the next two years (and vice versa).
See https://viewfromthewing.boardingare...r-marriott-and-starwood-credit-card-approval/
Then, after you are 5/24, and assuming no SPG/Marriott cards, I would focus on the Amex SPG cards and avoid the Chase Marriott cards for now, and maybe try for the Chase Marriott cards if you can get back under 5/24 in about two years. The reason for this is there are currently 2 Chase Marriott cards (the Marriott Premier Plus and the Marriott Biz), and 3 Amex SPG cards (the SPG Personal, SPG Biz, and SPG Lux).
The bonuses are richer on the Amex SPG-side too. If you go through all 3 Amex SPG cards, at their current offers, that’s 275k Marriott points from the welcome bonuses alone. The
SPG Biz currently has a 100k Marriott points after $5k/3 months MSR offer, first year annual fee waived (offer expires 10/31/18); the
SPG Personal has a 75k Marriott points after $3k/3 months MSR offer, first year annual fee waived; and the
SPG Luxury has a 100k Marriott points public offer (125k Marriott points targeted offer) after $5k/3 months spend, $450 AF not waived. Keep in mind the SPG Personal is supposed to be discontinued sometime in early 2019, when the Starriott brands completely merge and Chase gets the consumer and premium consumer cards, and Amex gets the super premium consumer and small business cards. If you go for the Chase Marriott cards first, you disqualify yourself from the Amex SPG cards and won't be able to hit the SPG Personal card and bonus before it's discontinued. While some people suggest waiting for the SPG Personal to raise its offer (because 75k Marriott is equivalent to the old 25k Starpoints offer), there’s no telling how much longer the SPG Personal card will still be around. But maybe Amex will make one final push to attract signups with a higher offer for the SPG Personal before discontinuing the card?
The Chase Marriott cards are both offering 75k Marriott points right now with a $3k/3 months MSR, AFs not waived. (Compare with Amex SPG Personal and Biz cards that waive the first year AF.) That’s just 150k Marriott points combined.
Getting one of the Amex SPG cards has no preclusive effect on getting another SPG card under the post-8/26 rules. But it will disqualify you from getting a Chase Marriott card for about 2 years. Remember, Amex welcome offers are generally once per lifetime, so you won’t be coming back to churn those cards again. Getting the SPG Personal and Luxury will add cards to your */24 count, but they’d make you ineligible for the Chase Marriott cards for 25-27 months (24 months after bonus received) anyway. And in about 2 years, these cards will drop off, and assuming you're under 5/24, you can see about going for the Chase Marriott card(s) then. Note that by then, Chase will probably have discontinued the Marriott Biz because the small business card product is supposed to belong to Amex. But perhaps Chase will raise the Marriott Premier Plus back up to 100k Marriott points at some point?
3 > 2
