I would suggest she start with applying with a credit card from a bank or cu she currently banks through as she would have some relationship established with them and is more then likely to get approved for a credit card and maybe even with a good SL. That's where I would start, then give it 6 months to a year of on time pif payments then try for better cards which she wants, this worked with my sister while she was around that age. As someone else said you could also check pre-qualified offers from banks if you insist on a "better" rewards type card to start with.
Start with either a secured card or check pre approvals from banks like Discover also as somebody else said try checking for card offers at the place she banks. If she has a good history with them they may approve her and then she can build her credit up.
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First things first. Obtain her real Fico scores.
Welcome @Anonymous. 
Your SO is in great shape for a nice first card. I like the idea of checking into Amex, Discover, and Capital One prequals. I'd skip Capital One, however, unless they offer a good card. I also like the credit union idea. She absolutely does not need to be looking into secured products.
She should probably stay away from Chase unless she's willing to risk a denial. Some get approved early, but for the most part, Chase really likes to see a full year of card history.
@Anonymous wrote:Wondering what the best first credit card for my SO would be so she can start/continue to build her credit?
Background: She's 21, has made around 25-30 on-time payments on her vehicle that's in her name, and has a couple years of on-time utility and phone bill payments. She's never had a credit card before or anything negative on her credit. She has no debt other than what's left on her vehicle. She's looking to apply for her first CC to help build her credit. She is very responsible and is employed full time as a police officer. Though it's not too important to her at this point, cash back would interest her most with earning miles coming in second.
What are your suggestions?
Who is the lender for her auto loan? I would suggest seeing if they offer credit cards since she has such a good payment history with them or like someone else said check with her current bank or cu or just check the offers for capital one , amex or discover.
