The performance of a hosting provider will depend on what you're buying from them. For ex if the bottleneck is bandwidth, that might be OK for a CPU-heavy server rendered app without many users but horrible for a popular app with a heavy js payload. If their database offering is slow, that only matters if you're using it. Etc.
The best way of producing a ...
The best way to do this is to use a subdomain e.g. shop.example.com and in DNS point the A Record for that subdomain to the IP address supplied by shopify.
Then the regular website will be at example.com and it should have a link to shop.example.com which will be the shopify shop.