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Harrison's and TOP's Flight are both solid choices that most finch owners seem to trust, though you'll want to mix them with some fresh veggies and seeds since finches do better with variety. Pretty much any brand that's made specifically for small birds and doesn't have a ton of artificial dyes will work fine.
Skip the cheap colorful pellets from big box stores - those dyes are unnecessary and finches don't need them.
The thing people often overlook is pellet freshness; even good brands like Harrison's go stale if they've been sitting on a shelf too long, so check the date and store them in an airtight container once opened.
Stick with brands that focus on natural ingredients without artificial colors, and yeah, mixing pellets with some greens and the occasional seed treat keeps them happier than pellets alone.
I've had decent luck with Zupreem and Harrison's when I can find them fresh - the key thing I noticed is that pellets absorb moisture and go stale pretty quickly, so I check the manufacturing date before buying.
One thing that caught me off guard was how picky my finches were when I first switched them over; they need a gradual mix-in with their old food or they'll just ignore the new pellets entirely.
The colorful dyes definitely seem unnecessary, and honestly the birds don't care about presentation, so sticking with the plain pellets and adding variety through things like millet, greens, and the occasional seed treat seems to work better than trying to make everything pellet-based.
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