umm core i3 is a very bad buy for gaming actully. Its a dual core solotioun and hyperthreading isnt a true quad core, never will be. As more and more games take advantage of 3 or more cores which is happening the Athlon X4 even beats the Core i3. The Core i5's only notable chip is the i5 750 and even then its the same price as a Phenom X6 which regurally beats the Core i7 965.
1. Few games use more than 2 cores. Ive seen Dual Cores beat out my Quad in games. An overclocked Dual Core is of more use than a slower quad core for most people. You say games are beginning to take advantage of quad cores, but look at what happened with dual cores. It took years to get them to use even 2 cores, and it's going to be the game for this iteration too. For the next 2 years at least, a Dual Core will still be better than a quad for gaming (at the same price level)
2. In most applications, even a i7930 will beat the X6 like there's no tomorrow. If you use applications that can take advantage of 6 cores, then it will likely be faster than a similarly priced i7, simply because it has more cores. Clock for clock though, its much slower. The X6 is a K10 part which is almost 3 years old now. It was also never very competitive with the Penryn series of architectures from intel. When it came to the Nehalem the K10 is hopelessly outgunned. The only thing AMD can do from here is bump up the number of cores while they develop a new architecture.
3. Phenom II X4 beats the i3's for the most part yes, but the i3's werent meant to compete with the X4 parts. Even then, the i3's have a lower price point than the Phenoms do, and they are very competitive at the clock-for-clock level.
4. If you buy a modern cpu, and you are not completely computer illiterate, you should try overclocking it, even if just a little bit. Many of intels parts can get to much higher clock speeds (4.6gHz isnt outrageous) which is where they truly shine. At these speeds they seriously outpace even overclocked AMD parts.
I do agree with your assessment of RAM. You will need DDR3 either way with a modern CPU/mobo and their prices are fairly comparable now due to the rise in demand for DDR3.
From someone that has 8GB of RAM, unless you do a lot of audio/video/graphical work, you will be quite fine with 4GB. Take the money you saved and instead get a 40-60GB SSD, it will give you a much better boost in performance.