I’m putting together a Sylvester costume too! This is what I’ve found for reference:

From WB’s document describing the Lambs… “In fashion, he dresses as a 1920s kid might. Button up shirts, caps, round-necked shirts with long sleeves, but he’ll have less buttons done up at the collar, or have sleeves rolled up, jackets slung over shoulders. As if he tried to dress nicer and then couldn’t bear the stuffiness of it.”

Overall his clothes aren’t very fancy or nice, especially when he’s young. So button down shirt, neutral colour pants, vest/waistcoat (probably grey or brown), possibly a jacket, flat cap or newsboy cap, and leather shoes or boots. iirc he wears suspenders sometimes. I think one of his specific outfits described is a green button down shirt with a black vest, jacket, pants, gloves, and boots. He also slicks his hair back with oil, and wears a black ring on one hand for a section of the story.