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I would split purchases between the two cards.
A challenge with working through low limits is that even making prudent purchases may mean high account utilization.
Until you get limits higher it might make sense to pay bills well before they are due in order to lessen utilization reported.
If you know on what days those issuers report to credit bereaus, I would suggest making online payment a few days before those dates. If you really want to optimize, pay off one card completely before balance gets reported. Make very small purchases on the other card but pay in full by the due date making certain the payment gets made in time.
To maximize FICO score you want all cards reporting zero except one card reporting more than zero but less than 8.9 percent utilization.
You want to show spending on the cards so that the issuers can justify credit line increases but you also need to get your scores up.
Discover gets my vote. It's 2% cash back for the first year (10% back on category spend). Congrats on your new Discover card! Don't worry about the $500 starting limit, it will grow. My son started with a limit of $1,000 and it's now at $5,500, all via soft-pull CLI requests.