One subject, half a dozen styles
Flowers are the most tattooed subject on earth, which means 'I want a flower tattoo' tells an artist almost nothing yet. The same peony can be a delicate fine line sprig, a bold traditional rose with thick outlines, a woodcut-style blackwork bloom, a scientific-illustration piece straight out of a botany textbook, a saturated neo-traditional showpiece, or a soft watercolour wash. Same flower, six completely different tattoos.
So start by working out which version you're actually drawn to. Save references, notice what they have in common, and then find an artist who specialises in that specific flavour, because a fine line florist and a bold colour florist are different specialists. Browse botanical artists by style and city on REAP's discover pages; twenty portfolios side by side will teach you the difference faster than any glossary.
Meanings, if you want them
The traditional associations, for those who like them: roses carry love and beauty, with the colour shifting the meaning; peonies carry wealth, honour and romance, and are a staple of Japanese tattooing; chrysanthemums carry longevity and joy; lilies carry purity and remembrance. Lotus, poppy, sunflower and orchid all have their own folklore. Worth knowing: these meanings are traditions, not rules, and they shift between cultures. The chrysanthemum is imperial in Japan and funerary in parts of Europe.