Which CheckedListBox event triggers after a item is checked?

You can use the ItemCheck event, if you also check the new state of the item which is being clicked. This is available in the event args, as e.NewValue. If NewValue is checked, include the current item along with the collection proper in your logic:

    private void checkedListBox1_ItemCheck(object sender, ItemCheckEventArgs e)
    {                     
        List<string> checkedItems = new List<string>();
        foreach (var item in checkedListBox1.CheckedItems)
            checkedItems.Add(item.ToString());

        if (e.NewValue == CheckState.Checked)
            checkedItems.Add(checkedListBox1.Items[e.Index].ToString());
        else
            checkedItems.Remove(checkedListBox1.Items[e.Index].ToString());

        foreach (string item in checkedItems)
        {
            ...
        }
    }

As another example, to determine if the collection will be empty after this item is (un-)checked:

private void ListProjects_ItemCheck(object sender, ItemCheckEventArgs args)
{
    if (ListProjects.CheckedItems.Count == 1 && args.NewValue == CheckState.Unchecked)
        // The collection is about to be emptied: there's just one item checked, and it's being unchecked at this moment
        ...
    else
        // The collection will not be empty once this click is handled
        ...
}