As long as the Server Type is set to Forge and the Forge Version is set to 47.1.3 under Configuration → Server Settings, it will start properly.
The Jar needs to be set to Autoselect and the Forge version needs to be filled out properly for AMP to start the server. (due to the Forge changes after 1.17)
That is common with large modpacks, not a fault of AMP.
You should be able to try re-joining a few times to see if that gets things working, otherwise add the following Java argument to both the client and the server: -Dfml.readTimeout=180
In AMP just under Configuration → Java and Memory → Additional java options
Then for the client you just google it, as each client does it differently.