It's not really a sawing motion but merely pulling a knife through something, it's just that I find the sawing motion an easier way for people to understand it usually. This is compared to having only one part of the knife contact something pushing down on it to cut which is a push cut which is where the polished edges shine. For now though I wouldn't worry about a higher grit stone as thats just going to complicate things by adding in more chances for a mistake to happen and were talking small differences in performance that most people won't notice.
A basic 2 sided stone with a coarse and fine side would do well, a good one for your application will probably be a Norton India stone which is suppose to be pretty good, I own the cheap economy version and this is suppose to be an improvement of it.
I would still pick up a DMT Aligner clamp to help you with getting the motion down for sharpening knives as it helps you develop the proper technique, and you can use this with a stone and all you need is the clamp which cost a little over $10 last I checked and is money well spent (though that does mean reprofiling most likely to some extent most likely if the angle isn't the same as this).
I would also recommend practicing on some kitchen knives you don't care about or picking up a budget knife to practice on, I would recommend a kitchen paring knife like an Opinel, Old Hickory, Victorinox if you wanted a dedicated knife as the steel in those knives have a decent heat treat and will reward proper technique with a sharp blade.
Than for the strop I already covered some of the things you can buy to use as the backing to it, but as to the compound I would say pick up one compound for now to keep it simple as well. Most people probably would say something like a green compound, I personally swear by black compound which is even coarser as a matter of personal preference. When I generally take my knives to a strop it's because they already started to dull and I want to remove a little bit of metal to prolong how long it is till I need to sharpen again on a stone. It's all a matter of personal preference but I would just get 1 compound that's at least as coarse as green compound and experiment on how you like to strop.
Also don't underestimate what you can do with a strop and good technique. I have to use a box cutter at work and I work 2 jobs doing stocking so I use the box cutter a lot and I am still using the original blade for for Gerber EAB for about 6months and had to take it to the stone 1 time and have just been stropping it. And that is with some pretty heavy use. A lot of my knives rarely touch a stone after the initial reprofile as I can generally bring back almost the full level of sharpness out of most of them from just a strop. It's quicker, easier, and I remove less metal.
Biggest thing to do at this stage is pick something and practice with it and try not to overcomplicate the process as your learning and experiment and find out what works for you preferably before you invest too much in a setup you find that doesn't work for you. Just keep in mind everything requires some level of technique and if you find something that you like using stick to it even if your not currently getting the results you want instead of switching several times. It's far better to stick to learning one thing and mastering it than trying to master 10 different things. And you can read up on sharpening all you want and gain all the knowledge in the world about sharpening but it can't replace practice so be sure to do that, preferably not on your nice knife do that after you feel comfortable. So stropping isn't too dangerous most likely so practice a little on other knives and than use the sharpie trick and go ahead and strop the nice one for now to hold you off.
I also found some cheap drawer liner worked pretty good at propping a stone up and keeping it in place if you don't want to spend much money on a stone holder and ran into this problem. I would also look into the sharpie trick where you mark up the bevel and your goal is to remove it. This acts as an indicator that you are hitting the bevel, that's it in it's most simplistic nature for the use of a sharpie. When you are reprofiling it helps in telling you that you have removed enough metal that you should be apexing the blade or close to it after you remove it all, especially in a guided setup this helps a lot as you generally have more precision.
Heres a few links to people who know how to sharpen and do a good job at teaching it, some of them are members here too.
MrEdgy
https://www.youtube.com/user/MrEdgy81/videos
Neuman2010
https://www.youtube.com/user/Neuman2010/videos
jdavis882
https://www.youtube.com/playlist?list=PLB95E1C271CE6654B