My advice, for what it's worth, is this..............
continue using your current software, but I could almost guarantee that after a while, you'll notice it's limitations and want something more comprehensive. Lightroom and photoshop are essentially the industry standard these days (I know, there's lots of other software solutions in use as well

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Lightroom is a fantastic programme, which not only allows you to edit but also helps maintain a catalogue of your images, etc. Photoshop is the ultimate manipulation tool, very complex, but incredible useful in certain circumstances. (btw, lightroom editing engine is basically PS camera raw). Will you need both, certainly not to begin with, but that need may come eventually. I use the creative cloud deal, so get both plus extras for £8.78 per month. Some people think this is a great deal, me included, others think it is not and prefer perpetual licences............ each to their own.
Regarding, jpeg or raw, I'd always opt for raw unless I need to shoot fast moving sports, etc. which I'd use jpeg for, so I can ensure that my camera buffer does not fill up as quickly. Raw does not contain any edits by the camera (even the preview you see on the camera screen, when shooting raw, is a jpeg image with default settings applied) and when you import it, you may be underwhelmed by the lack of contrast, sharpening, etc., but the big plus is that you have much more latitude when it comes to editing. With LR you can, if wanted, automatically have an import preset applied to the raw images so that they look more like the camera jpeg and then do further work on the image or multiple images at one time.
Basically, my rational is that, I want to get in right in camera, but for those times when I can't, I want as much control over the editing of the images as possible and the raw format does that for me.
As with a lot of things in life, there is no right or wrong answer, only a solution that works best for you.