Below is the example of LTM policy to redirect from one host to another.
There are few things to consider here-
-The redirect policy / irule will change the hostname/URL in client's browser. So the redirected host should resolve the correct IP address from client system in order to access the page.
-As you said the redirected host will be the hostname of the server in F5 Pool then mostly it will be internal host only and if your client will access it from public internet then it can cause issues as internal hostnames won't resolve any IP from internet. I am considering the normal case here.
-If you want client's request to be send to internal hostname but client shouldn't see the internal hostname then rewrite option will help you.
-Additionally if you configure normal pool with IP address or FQDN of the backend server and map it to the vServer. Then request will be send to backend pool member IP. In this case , it is not require to setup any kind of redirect policy or iRule to forward such requests.
Hope it helps!