Replying to Photo editing help

I've been taking pictures for a few years now, I started shooting film and loved it, however after a while it simply became too expensive for me to keep up with exclusively so I bitched out and bought a digital camera.
One of the reasons I loved film is the lack of editing required, I would get a roll developed and any keepers I could just upload. However shooting digital I find myself needing to tweak them before I get them looking the way I want. As of now the extent of my editing knowledge is using VSCO on my phone, which works find for just instagram, but I would like to start being a little more professional and getting my stuff out on flickr and such. However I have no idea how to start being more professional about my editing. I have a basic Asus laptop so I'm not sure what programs I would even be able to run.
Any advice would be much appreciated!