Are there any artists here who can recommend a slightly nice set of markers that don't cost upwards of $400?
LORDY YES.
POSCA brand markers are fun to play with, they're totally opaque, $30-50.
Tombow makes some Dual Brush Pens that are essentially water-based markers. There's a detail pen and a brush pen on each one. $25 per set, pick groups of colors you think she'll like. I spent hours coloring in rubber stamp images with these when I was her age.
Michael's brand Artist's Loft has a set of 12 Color Dual Tip Sketch Markers if you wanna give her the feel of fancy Prismas or COPICs for a lower cost. They're alcohol based markers and she'll have plenty of fun with them. $50.
Sharpies are honestly fine for most projects [but maybe not for a 6 year old??]. Fine tip would be good for developing her fine motor skills! $20.
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Until our souls cross paths once more in the boundless sphere of fate.