Three ways to do it:
A somewhat better WordPress way would be to apply a generic filter to the input and then apply wp_filter_kses to the filter. Like this:
$hello_greeting = apply_filters('hello_plugin_greeting',$_REQUEST['hello_greeting']));
... later, outside all the other functions ...
The advantage here is that extra filters can be added or removed from the hello_greeting value in real time.
Finally, there is an easier and simpler alternative all around. In the specific case of "options", WordPress has a function called "sanitize_option" that all option values must pass through. You can hook into that with a plugin and automatically run your option through kses. All you need is one line of code, outside all the functions:
Do that for each option you use.
Which one of the above three methods you use is up to you, each has advantages and disadvantages.