A very popular free one that I've used before is Synth1 (yes, that's literally the name of the plug-in). It's got all the features you would expect from any basic synth, plus a few other features that are more advanced. It also has downloadable presets up the wazoo, which I find to be good starting places for sound design projects. It is worth noting that there are actually a ton of great free plugins all over the internet, so if you find some that you like, you don't nessesarily have to spend any money on anything. In terms of software, I don't think there are a ton of free options. In my experience, LMMS sucked and cakewalk had issues with some of my plugins. MuLab might be better than those two, but if I remember correctly it limits free projects, and you have to pay a (relatively) small sum of money to get rid of the restrictions. If you're looking into payed options, there are a ton more of them, but you have to do your research or you might get stuck with something you barely use.
Speaking of which my goto VST has forever been Cakewalk Z3ta. It's very good at "Crisp" and "Digital" sounds, has a big two page mod matrix, and pretty much everything I need. I've bought a bunch of VSTS since then, but I still use Z3ta the most.
Purity, Nexus, Omnisphere, ElectraX, Ravity, Wavestation, M1