I have three credit cards. The first two I opened have a limit of $500 each. The one I newly opened has a $4200 limit. What could this mean for building credit scores?
For scores, nothing directly.
But it can help you manage your aggregate utilization, which would affect your scores.
And it could look better if you go through a manual review for higher limit cards
In the short term, the opening of accounts usually drops scores. You mentioned the credit limits, suggestive that they may impact your Fico scores. The limits don't help build your scores. If those $500 limit cards were $5000 limit cards and your $4200 limit card was a $14,200 limit card it wouldn't be any different in terms of how the algorithm looks at those revolving accounts.
Yes, higher limits DO affect your scores, as long as you keep your usage down, in other words you can use more of your credit without your score taking a hit, and the increased available credit often ups your score because it makes your usage percentage go down immediately.
That's only true though for profiles where utilization isn't already in an ideal place. If it's in an ideal place before greater limits/CLIs kick in, it's going to remain in an ideal place after and there will be no scoring increases.