Everyone said a lot of great stuff.
Gene looks like he wants to get somewhere in a really short time while working out the strategic things.
In order to make spin variation, one must actually have heavy spin (or a damn good appearance of it) and very light to no spin to have that wide range or variation. That means showing your opponent some really heavy underspin. You establish that your first chance, then go from there.
In order to make it work, the other player has to THINK the change in spin isn't happening, or at least to the degree it is. That means your serve motion must be smooth and fluid and look the same for each spin. That requires some timing and touch.
It is also possible to fool someone on how deep or shallow you are serving. That means you gotta be able to serve both short and deep. Just off end is good change too. To be able to fool anyone, that means you gotta have some control over your depth. That requires touch and timing.
These are all great things to work towards improving over time, but no one really makes instant gains. 3 months, however, is a lot of time and a good deal of progress can be made towards those strategic goals. Some thought and execution can also result in some near term improvement in this in an area.
The simplest to execute for newer (or returning players) is FAST and DEEP serves. The serve motion is fast. The ball moves fast. There is little time for opponent to figure stuff out. If the placement is right, he has to move AND read the ball AND make a return, which is likely gunna be long, just right to get into a fast rally or make the first decisive fast attack. You might get some errors.
This has the biggest bang for the buck at first. A couple weeks of practice getting the motion, impact and blade angles right can get a player to do alright with those. These SUDDEN and FAST/DEEP serves are WAY more effective when the player can serve short at will (and also vary the spin, placement, and keep it low enough)
Being able to serve short or half long takes a lot more time to get the timing and touch down, but a lot of progress can happen in three months.
I recommend AGAINST starting out at the table to learn short underspin serves. WHY? A player who doesn't serve short doesn't have the touch and the blade angle to do it without nearly stopping the blade before impact for a weak dead serve that is obvious. I see player after player struggle to learn of make any progress doing it this way. The most common error is to NOT have blade parallel to ground at impact. Players who do this NEVER fix this at the table, even after months of trying. They are too worried about getting ALL the stuff of the serve perfect and it isn't gunna happen.
The important things to be able to get right are the blade angle at impact (completely under the ball at the bottom) the swing direction (completely forward), the timing of the swing to target, the timing of the moving parts of the arm/wrist, and the touch - this is the grip and the ability to accelerate the bat in a very short distance. The object is to get the ball to penetrate the topsheet, and while wrapped by topsheet, accelerate bat and fling it out.
I recommend a layered approach in steps. After learning the basic breakdown of how to use the arm (use short forward swing, stop upper arm at a point and hinge lower arm on elbow to move forward,, then use a little wrist right before and during impact)... after learning the basics there are a few ways to do progressive exercises before going to the table.
First step is an exercise that promotes a very simple forward swing void of many moving points and works the barebones essentials. You stand up on an area away from the table. A hallway, and open room, or at teh club away from the table, behind the table wherever. You do a ball toss head height, have the upper arm already moved forward to teh target impact zone, (lower arm is back some), and swing forward with a totally open blade parallel to floor and impact ball using mostly lower arm, use more wrist as timing and feel develop. You are trying to send ball out 1-2 meters with underspin, then make it spin back to you. This works the basics of mechanics, timing, and touch. There is no better way I have found to start out to develop this at the early stages. DO THIS DRILL 15 MINUTES a DAY. You will be a lot better and discover/reinforce proper blade angle at impact and the mechanics/timing/touch/acceleration... you will grow 10x faster doing this than learning at the table where there are too many things to worry about at first to focus on the basic important stuff - mechanics / blade angle at impact / timing. The acceleration and touch will improve much faster when you get the mechanics / swing plane / blade angle right. They will improve with more practice if you can get the foundation. Getting the right motion and impact to result in heavy spin are the goals, not the height control - that comes later.
Doing that even half-azz can take month or more. DO NOT GET DISCOURAGED. No one, I mean NO ONE failed at this more than I did at first.
Next stage is to practice a bit off the table. You stand a meter or more behind the table then you do the same thing, but you are flinging the ball forward to land on your side, then the other, then spin back on your side. You are letting this thing bounce really high. That is OK. At this point, you are simply trying to make heavy spin and get the impact and mechanics right. height control is not important yet. You are trying to show yourself you can make heavy spin at will and make it bounce on both sides, while you are overall getting better at your mechanics striking the BOTTOM of the ball with a short forwards swing and improving the timing/touch.
This also takes a goodly amount of time, a month or more to get to the table.
Once you are at the table, a progressive approach is also good. DO NOT WORRY about height control. You are simply practicing getting the basics of your swing and impact right... or right enough while improving over time. You should get right up to the table at your BH corner, do the ball toss to head or higher height, and use a short forward stroke to impact the bottom of the ball with better lower arm and some wrist. Aim for a little past half way to the net for first bounce. Let the ball bounce high, it is OK at this point. You want to grow your basic mechanics with a ball toss close to the table... don't sweat the rest of the stuff.
This is a minimum of a few weeks. Don't worry about being perfect, just strive to improve the ball toss, timing of the mechanics, the blade angle parallel to ground, the timing/touch of the impact, and the general area of the first bounce. You are serving it high, and ghosting it back t the net. Once you can ghost it back to the net and sometimes make it bounce back to you coming back OVER the net, you are ready to try it out at combat speed.
At this stage, you are trying one by one to get the other fine point stuff down - because you have the basics down, this is easy stuff over time to improve. Not easy at first, but you will see progress if you got the basics down. Try out different first bounce points, but stay in the same general zone of just past halfway to net. Do not worry about being super low over net, this comes with more reps and developing better touch and timing if your mechanics are right. LOOSE grip is uber important, so are loose muscles to make the whip. Once you get the hang of it, you will see it is WAY easier to make short serves with the tip of the bat pointed down to make side/under spin.
Later on, months down the road, you can learn how to impact the ball WITHOUT much acceleration (to make a dead ball or a very light ball) and immediately and naturally follow through with acceleration real smooth to fool opponents making them think you made a heavy serve, but it was a HEAVY NO-SPIN.
Once you get to that point, all kind of doors will open for you on serve and 3rd ball.
More on all this stuff later. Those are the basic concepts and way to go at it with a plan to make good progress in 3-4 months with only 15-20 minutes of practice a day.
I had only 3-5 minutes of practice a day for a year on one of my Iraq trips to a camp, I improved 200 points USATT rating upon returning home without much match practice.