I would tend to agree with @uzaysan and I would add that if you have little experience with AWS, managing backend infrastructure, scaling etc it may provide less headaches to go with a managed service. With both Back4app and Sashido you can spin up Parse Server and Parse Dashboard in minutes, they both provide easy configuration options, automatic scaling, backups and much more. Another advantage is that depending on your plan both providers offer support via email, chat etc.
However, I would also say that Parse Server is designed to remove complexity so if you have some AWS experience you should be able to get a basic Parse Server & Parse Dashboard setup fairly quickly. If you get stuck there are lots of existing resources in our docs, on this forum, on the parse-platform tag on Stack Overflow and in GitHub issues. Hosting yourself also allows you to make any customisations you wish for example you can maintain and deploy your own fork of Parse Server.
If I was you for your first project go with a managed solution and then as you get more comfortable with the Parse Platform you might want to try self-hosting.