Of those three, the only one I would even consider is the one in the middle. It has a Core i7, so it wins there, but the graphics card is not as good as the one I picked up for only $100. As @uberbatman already said, Alienware tends to be overpriced, and I would only pay $600–650 for something with those specs.
Personally, I am a fan of building my own, at least when I can find good deals on parts, but for that I would have an easier time making recommendations if I had a desired budget; something more specific than “as cheap as possible” since cost and quality go hand-in-hand. At the time of my last upgrade, I got a good enough deal on a pre-built to go that route instead.
For recording, almost any computer currently on the market will suffice. Hell, I could probably do it on my phone! But your hardware needs will depend on what else you plan to do.
FYI, lag is a function of your internet connection and LAN. Your computer’s specs have no bearing on ping times. Ferraris cannot go fast when they are stuck in traffic, if you catch my drift. If lag is your primary problem, find a better ISP.
Lastly, “gaming computer” is a marketing term. My PC was never intended for gaming, but after just a little work, it can beat many rigs that are marketed as “gaming PCs”.