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Interchangeable circular needle setChiaoGoo Red Lace and Knitter's Pride Karbonz are the two sets that knitters actually keep using years later. Metal tips, smooth join, interchangeable cables.
Merino yarn (fingering/DK)Superwash merino at fingering and DK weight is the workhorse of knitting. Wearable against skin, machine-washable after treatment, holds stitch definition.
Row counter + stitch markersA locking stitch marker set and a clicker row counter cost under $10 combined and prevent most beginner mistakes. Get more markers than you think you need.
Blocking mats + T-pinsWet blocking is the step that makes knitting look finished. Foam mats with T-pins hold your piece in shape while it dries. Blocking wires help on shawl edges.
Swift + ball winderIf you buy yarn in hanks, a swift and ball winder are not optional after the third time you tangle a skein over a chair back. The Knit Picks set is the budget entry point.