it's imposible to know if search settings are correct or not with only a vague description that you are not getting the results you want, I needed to know specifics of the results you where getting versus what you expect to be able to determine if the settings are correct or not.
I suspect the problem is not the settings, but rather the data.
your search for "First Aid Kits"
will only retunr results that include the word "kits"
whereas "First Aid Kits" will return results where the word "kit" and "kits" is included.
theres not really a way around that except to use a products keywords column where you define all the key words that can be used to search for an item so that you can specify that an item be returned whether search is for "kit" or "kits"