If you're trying to write portable shell code, your options for string manipulation are limited. You can use shell globbing patterns (which are a lot less expressive than regexps) in the case construct:
export LC_COLLATE=C
read word
while
case "$word" in
*[!A-Za-z]*) echo >&2 "Invalid input, please enter letters only"; true;;
*) false;;
esac
do
read word
done
EDIT: setting LC_COLLATE is necessary because in most non-C locales, character ranges like A-Z don't have the “obvious” meaning. I assume you want only ASCII letters; if you also want letters with diacritics, don't change LC_COLLATE, and replace A-Za-z by [:alpha:] (so the whole pattern becomes *[![:alpha:]]*).
For full regexps, see the expr command. EDIT: Note that expr, like several other basic shell tools, has pitfalls with some special strings; the z characters below prevent $word from being interpreted as reserved words by expr.
export LC_COLLATE=C
read word
while expr "z$word" : 'z[A-Za-z]*$' >/dev/null; then
echo >&2 "Invalid input, please enter letters only"
read word
fi
If you only target recent enough versions of bash, there are other options, such as the =~ operator of [[ ... ]] conditional commands.
Note that your last line has a bug, the first command should be
grep -i "$word" "$1"
The quotes are because somewhat counter-intuitively, "$foo" means “the value of the variable called foo” whereas plain $foo means “take the value of foo, split it into separate words where it contains whitespace, and treat each word as a globbing pattern and try to expand it”. (In fact if you've already checked that $word contains only letters, leaving the quotes won't do any harm, but it takes more time to think of these special cases than to just put the quotes every times.)