Multiple Websites on Single VIP

I just noticed you wanted to account for www in your HTTP-HTTPS redirect so here's an update example for that irule:

when HTTP_REQUEST {
    if {[string tolower [HTTP::host]] starts_with "www."}{
        set host [string range [HTTP::host] 4 end]
    }
    else {
        set host [HTTP::host]
    }
    set my_loc "https://$host[HTTP::uri]"
    TCP::respond "HTTP/1.1 301 Moved Permanently\r\nLocation: $my_loc\r\nConnection: close\r\nContent-Length: 0\r\n\r\n"
    TCP::close
}

The irule for the pool selection on your HTTPS VIP could look something like this:

when HTTP_REQUEST {
    switch [string tolower [HTTP::host]] {
        "site1.test.com" {
            pool site1_pool
        }
        "site2.test.com" {
            pool site2_pool
        }
        "site3.test.com" {
            pool site3_pool
        }
        default {
            pool default_pool
        }
    }
}

Hope this helps.