I have a client who uses Celerant. It does the job and integrates the POS system in his store with his online catalog with his Amazon catalog.
His legacy version requires a dedicated server, but it looks like new installs would be cloud-based. But at $250/month ($350 if you want POS integration), you can get a lot of Shopify for that price.
I think LM is right - Shopify is probably the past of least resistance. You can integrate your POS, online store and Amazon inventory.