Just use
If @searchType is null means 'return the whole table' then use
WHERE p.[Type] = @SearchType OR @SearchType is NULL
If @searchType is an empty string means 'return the whole table' then use
WHERE p.[Type] = @SearchType OR @SearchType = ''
If @searchType is null or an empty string means 'return the whole table' then use
WHERE p.[Type] = @SearchType OR Coalesce(@SearchType,'') = ''