How to remove files starting with #! or ending with .sh in the name - shell

Question

I am new to shell programming. I want to move any executable file, any file starting with shebang(#!), and any file whose name ends with .sh from a directory to /tmp/backup and log the names of the files moved.
This is what I have done till now
Searching for files with #^
grep -ircl --exclude=*.{png,jpg,gif,html,jar} "^#" /home
Finding executables
find . -type f -perm +111 or find . -type f -perm -u+x
Now I am struggling how to club these two commands get a final output which I can pass to perform backup and remove from current directory
Thanks

Answer 1

Use the xargs command
"find command" | xargs "grep command"

Answer 2

You could put everything in a file, sort it, then process it with Awk:
# Select all files to move
grep -ircl --exclude=*.{png,jpg,gif,html,jar} '^#\!' /home > list.txt
find /home -type f \( -perm -u+x -o -name "*.sh" \) -print >> list.txt
# Feed them to Awk that will log and move the file
sort list.txt | uniq | awk -v LOGFILE="mylog.txt" '
{ print "Moving " $0 >> LOGFILE
"mv -v --backup \"" $0 "\" /tmp/backup" | getline
print >> LOGFILE }'
EDIT: you can make a formal script out of this skeleton, by adding some variables and some additional checks:
#!/bin/bash
LIST="$( mktemp || exit 1 )"
LOG="/tmp/mylog.txt"
SOURCE="/home"
TARGET="/tmp/backup"
mkdir -p "${TARGET}"
cd "${SOURCE}" || exit 1
# Select all files to move
grep -ircl --exclude=*.{png,jpg,gif,html,jar} '^#\!' "${SOURCE}" > "${LIST}"
find "${SOURCE}" -type f \( -perm -u+x -o -name "*.sh" \) -print >> "${LIST}"
# Feed them to Awk that will log and move the file
sort "${LIST}" | uniq | awk -v LOGFILE="${LOG}" -v TARGET="${TARGET}" '
{ print "Moving " $0 >> LOGFILE
"mv -v --backup \"" $0 "\" " TARGET | getline
print >> LOGFILE }'