Yes, Shopify is a legit company. They are publicly traded at the NYSE. So yes, it’s safe to do business with them. You can test Shopify for free. However, once you upgrade, do keep in mind that, unlike most other site builders, they don’t offer a money-back guarantee.
Another thing to be aware of is that there is a small number of Shopify stores that are run by scammers. And although Shopify is closing down these online shops regularly, they can’t catch every fraudster immediately.