Honors LLC is not any more competitive than the others. Basically as long as you apply to any of them before they are full you will get in. Look into the dorms as well. Each LLC is in a specific dorm and this may help you decide (apartment, standard, etc) and look at location of the dorm.
The research component seems unimportant as anyone who wants to do research at Tech can typically get it. It is not hard to get as an undergrad at all.