What is the best strategy for starting up an online storefront for a startup clothing brand?

With no overhead. Your core competence is the apparel, not a website, right?

So head over to BigCartel or Shopify and make a freemium store. Pay them per purchase or inventory item, and keep costs down as you figure out your customer acquisition machine.

You'll also get an array of brand styling tools, merchant services, and so forth which will come in handy if you aren't tech savvy or don't want to piece together an e-commerce platform from scratch (you don't).