How much does it cost to host a backend with database, cache and few VMs and a frontend? Expecting avg daily visitors 1k initially?

You can use the AWS pricing calculator to calculate it as per your exact needs & use case:

https://calculator.aws/#/

The only way to get a good estimate is to analyse your service.

That being said, for 1k visitors why don’t you just use vercel + supabase? Free tier should cover it, and if you have any compute heavy stuff just move it to a lambda or a separate instance on AWS.