Try to get at least $200 out of each card. A lot more than that if you will continue chasing sign up bonuses over the rest of the year. In a few minutes looking I see:
> Bank of America Cash Rewards credit card that is $200 cash for $500 spend,
> MLB version of ^ the above, also $200 for $500
> American Express Blue Cash Preferred® Card, $200 for $1,000
> Wells Fargo Cash Wise Visa® Card, $200 for $1,000
If you plan to do this going forward you will find yourself trying to get the greatest bonus per card application, rather than just looking at per dollar spent. That is why most of the cards you see recommended are more on the order of "$500 for $5,000 spent" or something. The best pure cash back strategy I have thought of involves racking up a huge pile of American Express Membership Rewards Points, and then transferring them to Schwab at 1.25 cents each. But to get the most out of it will involve three or more cards with $12,000 or more combined spend, pulling in some side benefits, likely a year or two, and also some luck in being offered high bonuses.