Not a better way to go, but an additional way to go. Once you've picked an airline, get its credit card and use it to add to your mileage totals. Credit-card miles generally don't count toward status with the airline, but there are some exceptions - including, often, Delta. Other than that, cards tend to be similar enough that your choice of airline should come first.

Since it sounds like you don't charge enough for credit card charges to earn you rewards in their own right, stay away from cards that accumulate points in their own programs and that you can't combine with, or convert into, miles in your chosen airline program. The fine print can sometimes be obscure on this point, as the cards with that type of program don't like to trumpet their disadvantage too loudly.