Order of importance:
1) Technique and understanding of what's going on: first and foremost by far. This is demonstrated often by many people using various DAWs, different plugins, etc. ranging from free software (or iPhone apps lol) to the most insanely geared-out ProTools rigs.
2) Plugins: distant 2nd. And lots of free plugins these days sound fantastic (while not identical to more costly plugins which go to great lengths to emulate hardware). If you prefer a certain plugin, IMO there should be a reason for it which is based on personal preference (you've compared them and know what you like) or something that fits your workflow better in some way. There is no "best" for everyone.
3) DAW software: I'd say "3rd" but realistically it's not even on the list, in terms of audio quality anyway (preferred workflow is a different story of course). We're at a point in time where all DAW software should have the ability to sound the same (some might not, but probably all the ones you've heard of do). There are some exceptions sort of, like MixBuss. The thing with MixBuss however is that it has "built in" emulation of hardware on every channel whether you want it or not (presumably you would, if you're interested in MixBuss, since that's its major selling point). You can achieve similar things in Reaper or whatever other DAW software using plugins, but some people want it to "just be like a hardware mixing console".
There's no way around it--you'll be spending a lot of time trying different techniques and listening, comparing. Spend whatever you want with my blessing on DAWs and/or plugins; whatever works best for you for whatever reason, that's up to you. Just don't let flashy marketing and over-the-top reviews trump your own experience. I've heard plenty of mixes from people who thought they knew what they were doing, who were basically relying on their choice of plugins and hardware, and their mixes have just as many flaws as anyone else who doesn't have a good understanding of what they're doing.
Demo things if possible.
Use good headphones that sound very revealing (I recommend trying a bunch with the same source material and picking a set that works best for you). Fortunately this doesn't have to cost that much (maybe $200 or more if you want).
If your monitors (speakers) aren't great you may want to get something better. You can expect to pay around $1000 each for monitors which are "next-level" stuff for mixing. If that's too steep you can alternate between good headphones and whatever speakers you can afford, doing the pickier things with the headphones.
You may want to get a better audio interface depending on what you currently have. You don't have to go crazy but generally speaking you can expect to pay $800+ for an interface that's really going to be really good for mixing. I mean, if you want to really hear what's going on and not just say "close enough"...it's up to you. Lots of cheap interfaces these days sound fine, including $99 Behringer ones...you can get by with them if you want. I don't hear significant differences among the interfaces in the price range of $99 to $800 these days though; the differences are usually more about what features they have.
