Why not just pick one
Etsy provides marketplace search and a large audience of shoppers — value that can be difficult for a new standalone store to reproduce. It also charges listing, transaction, payment-processing, and sometimes advertising fees, while Etsy's systems determine how matching listings are ranked. Shops and listings must follow Etsy's policies and may face restrictions or suspension when Etsy enforces them. A standalone site gives you more control over presentation, but it does not begin with Etsy's marketplace discovery.
What integration actually looks like
The two can do different jobs. Etsy can remain a marketplace channel while a personal site becomes the brand's broader home: a fuller story, an events page, a press kit, or commission and booking forms tailored to the business. Links to Etsy listings or a clear "shop on Etsy" call to action can connect the two. A separate store can also support products and customer relationships that originate there, subject to its own payment, privacy, tax, and marketing obligations.
When to make the jump
A dedicated site may become worthwhile when a shop has repeat demand, needs functionality beyond its marketplace storefront, or wants a stable brand destination for wholesale inquiries, events, commissions, and press. Keep the channel boundary clean: Etsy prohibits moving a transaction that began on Etsy off-platform to avoid fees. Build the independent channel through your own marketing and customer opt-ins instead of redirecting Etsy buyers around Etsy's checkout.