@suds79. About the push variation.
(Firstly I agree with PierreAd that throwing in sidespin pushes here and there is often effective. It can be quite deceptive as to whether you're adding underspin or topspin to the sidespin... a bit like on serves, you can play with slight racket angle changes, or timing and/or point of contact.)
The deal is to make it clear that you can produce an aggressive, heavy backspin push. Then if you can generate a no-spin push that looks similar (or even just a 'normal' push!), you'll make the opponent miss a lot more (net/out), give you balls that are easier to kill (ball pops up) or easier to counter (opponent attacks more cautiously).
One of the many ways to do the heavy spin/no spin variation is as follows. Use a quick wrist motion upon contacting the ball, so that the blade face ends up slightly more open (almost horizontal) at the end of the action. If you do it right as you contact the ball (or very slightly afterwards), you should get very good spin. Overall the motion looks forward and down, with a bit of a tilt of the wrist in the middle.
Now if you change the timing so that you tilt the wrist just before contact, you'll end up giving a gentle hop/push to the ball instead of brushing it, which will greatly decrease the underspin or give light no-spin/topspin. You can still fake the forward/downward followthrough.
Make sure your pushes are generally aggressive and well-placed (corners, middle/elbow or wide). Start with deep spinny pushes and switch to no-spin as a variation.
There are variants, technically the trick simply involves going with a forward and down motion, starting with the blade face open but more vertical and ending up with the blade face more horizontal. The bat is overall going down, hence producing backspin (assuming you hit the back hemisphere of the ball as normal); except at the part of the blade closest to the table/furthest from the ceiling, which is moving upwards at some point while you are changing the blade angle. So the resulting spin depends on the timing and on the point of contact on the blade.
Again, there are other ways to do it as long as you can create a heavy backspin ball. You could also swipe under the ball and use some lateral wrist rotation to alter the spin. Depending on the position of your body with respect to the table you can add a lot of side-spin or a lot of underspin. Doing a simple cut under the ball but changing the blade angle by adjusting your grip beforehand can also work. Another simple thing given enough time is to deliberately vary longer, more ample strokes or shorter compact ones (especially with the forehand where you've got more room), which is in point of fact fairly unrelated to the spin you generate but can always get the opponent thinking

Same with stomping on the floor :3
edit. Of course you can also play with depth and height of your pushes to throw off the opponent's timing a bit. If you find it tough to keep your less spinny pushes low, you can always throw in a slightly higher, very spinny push once in a while. You just need to keep the opponent guessing.