It's worth remembering that FSX has a built-in "bias" towards Intel CPUs and nVidia video cards. I personally prefer AMD for both CPU & Video, but when in Rome... Since FSX is so old, there are a number of gotchas that I've heard of:
1) It can't make use of more than 2 cores of CPU. Still worth having a quad-core for the sake of other things, but FSX itself won't benefit from the other 2.
2) FSX won't make use of more than 4GB of RAM. Have yet to have this absolutely confirmed, but still worth doing 8GB of DDR3 dual-channel RAM anyway, so that FSX can have a clear 4GB to play with.
3) Due to FSX's age, it can't make use of quite a number of the advances in programming or architecture in the last 3-4 years. Again, still worth having "the latest" anyway, just don't expect FSX to be able to do much with the extra bells and whistles.
It appears that, barring a re-write by some enterprising individual, FSX will still be reliant on heaps of CPU GHz first, closely followed by a powerful video card (again raw through-put power vs one that is "efficient" due to it's new technology), followed very closely by using SATA3 64MB cache hard drives or SSDs, then followed by enough fast RAM.
If you didn't want to spend a bomb, I'd look at:
CPU - Upper end of the i5 series, remembering that for FSX it's the raw GHz speed (and a good-sized L2 cache) that matter most
RAM - 8GB DDR3 1600MHz dual-channel (Kingston's a good mid-range quality chip - just don't buy "cheap & nasty")
Video - Even the likes of a second hand GTX 460 will do very well, and these can be had from TM for around $150-$170 or $120 if the auction finishes at an odd time of day

Note that even some of the new GTX 5 & 600 series only just surpass the good old GTX 460, some extra "features" notwithstanding.
HDD - SSDs are still expensive, and how much extra scenery you have will dictate whether having FSX on an SSD will be a good idea or not. You could always have a fast 60GB SSD for Windows, a fast 128GB SSD for FSX, then a good (Western Digital is my preference) SATA3 64MB HDD for all the rest of the scenery.
PSU - Get a quality one that will give you at least 600W true with 2 x 12v dedicated rails AND Active PFC. AcBel make a fair range (in terms of quality vs features vs price), but so long as you're spending more than $120 on the PSU you should be going in the right direction. Warranty length is often a good indicator...
There's no doubt that an SSD definitely makes a good difference, but getting a truly fast SSD (one with both good sustained transfer rates and good burst rates) is not cheap. I suppose even a mediocre SSD is on balance better than a good SATA hard drive, but I've not been impressed with some of the cheaper SSD's performance.