I think your last solution sounds just about right. Get a budgeted PC now and then get a PS4 a year later or so. There are 2 reasons for this:
1. Next-gen consoles are just out for a few days. Their exclusive launched games are bad in my opinion, and it would take about a year or so for good exclusive games like God of War, Uncharted, Heavy Rain, Gears of War, Blue Dragon, etc... to come out. And believe me, those exclusives well worth the price of any console, Other launched games (BF4, Fifa 14, NFS Rivals,...) you could play on PC with no problems. And there would be some PC exclusives that worth your time and money as well (Starcraft 2, The Sims series, Dota, Counter Strike, LoL, The Witcher,...).
2. It's Christmas time, there should be tons of good deals for computing components. And I'm not sure if the launch of next gen consoles affect the price of components, but I hope it does lower the price.
That was what I did exactly 3 years ago, except that I went for a gaming laptop and quite regret my decision, but it served me well anyway. However, I think the life cycle of a gaming PC is much shorter than that of a console, so if you want a consistency gaming pc, you will have to prepare for costs of upgrades. Just a bit of information to help you make your decision.