Cobalt is correct. The three types are torturers, decievers, and militia.
The first two are rather self explanitory, the torturers are those who are keen on illusions that are designed to be less descrite and rather obvious, however they cause hellish pain that would generally leave the body incapable of movement. Paralysis through intense pain or destruction of limbs, hitting vitals that shut down the body. Tearing apart flesh, organs, creating situations that cause physiological shock like suffocation, etc. Voodoo Headless Chicken would probably be one of the best examples of a torturer's genjutsu
Decievers are self explanitory as well. They primarily utilize techinques that focus on decieving your opponent. Descrite techniques that are meant to fool the senses into either (a) making the surrounding enviornment seem as it it's unaffected while in actuality it is, (b) create a situation of false reassurance for your opponent, (c) hindering the senses in some way to prevent them from sensing something an oncoming technique. These techniques are typically designed to be more hidden and difficult to figure out for the sake of maintaining the illusion.
Torturers and Decievers attempt to maintain their illusions through their own methods. The former tries to prevent any movement from happening for a shinobi to disrupt flow through pain or genjutsu kai. This is presuming there are no summons or comrades/clones around to help. Decievers try to maintain their illusions by making sure their techniques are unseen/undetected therefore the opponent would have no inscentive to attempt any methods of release. Time Delay is perhaps one of the best deception genjutsu constructed that I've seen
Now Militia on the other hand, they are a combination of the two mentioned above. They use both methods of torture and deception. Depending on the situation they'll go for torture or deception or they may go for a combination of both. Quite recently I've been prone to the milita type. However I focus more on delaying my oppponent. Most genjutsu if not all are designed to delay your opponent in some manor for you to get the upper hand. Or rather, I should say confuse them to muffle their ability to react. With my genjutsu usage though, as most who have fought me, I fancy torturing to delay my opponents and cover fire/cover techniques to help me maintain the illusion while I go for another kill...doesn't work so much or at least when I've tried it, it doesn't appear to work.
So back to the initial question, as a genjutsu user what your goal is, for casting genjutsu and layering genjutsu, is dependent on your type as a genjutsu user and what you're going for. This question will probably more difficult for you guys to answer since you're not too seasoned in genjutsu, I mean you two don't seem like the type of people to use genjutsu regurally or enough so to deduce what you guys specialize in. When I first began my NB genjutsu training with Scorps I found myself more of a deciever, though I found out that wasn't the case. Upon paying more attention to my battles and genjutsu usage, I found I was more keen on torture. In order to tell your type, you're really have to look at how you use genjutsu.