I suppose it depends on what results you want. $1k is very light for FSX, although as I say, it depends on what you're expecting in terms of sliders vs frame rate. It appears that the general things to remember are this:
1) FSX is Intel / nVidia "biased", so you will get slightly better results with that mix vs AMD (I personally prefer AMD, but FSX demands otherwise if you want "best solution")
2) FSX is still very GHz heavy. Doug (or someone) posted on another thread that they reckon they can get FSX to make use of more than 2 cores of CPU. I've not achieved this myself, and usually the recommendation is to get a very fast dual core as opposed to a mediocre quad or more.
3) More than 4GB appears to be a bit of a waste on FSX unless you are planning on running other software at the same time
4) Doug says that the new raptor drives (as opposed to the older ones from a year or 2 back) are faster than SSDs. I've not been able to test this, and general "wisdom" is to have FSX on an SSD. Problem is even cheap SSDs of sufficient size are expensive. Also, one needs to get an SSD with fast throughput AND sustained transfer AND good burst rates. Bit of a tall order on your budget. Otherwise, an SATA3 64MB cache 1TB drive (my preference is Western Digital) is the only way to go.
There are some well-priced nVidia GTX 460's on TradeMe most days - that would be a good pick to help keep costs down for the video card side of things.
A note on hard drives: don't do the "cheap" thing of partitioning a 1TB into multiple "pieces". Most people think they're being clever doing this, not having to buy more hard drives. But partitioning a drive slows everything down a bit, and if you lose a partition it's more likely you'll lose other partitions at the same time or at least experience corruption. There is a bit of sharply divided opinion on this, but after having spent almost 20 years building / fixing computers (both Windows & Apple-based), I say that partitioning is from Satan's bottom.

Especially when it comes to performance / gaming.
Other things will sort of tend to take care of themselves, after a fashion, being governed by your budget. My personal preference for motherboard is Gigabyte, but many people like Asus. I won't use Asus as they are a pack of lying thieves who will do whatever they can to dodge warranty, but then plenty of people claim to have had no problems in that regard. They cost me $2k a few year's ago due to a crappy implementation of Vista on a high-spec'd laptop one of my clients was having major issues with, but they managed to hide behind all sorts of caveats & obscure legal technicalities that let them off the hook (even though they admitted that they were at fault, and they most certainly were). So I've been on a mission since to make them pay: $60k and counting: take THAT Asus.
Power supply needs to be over 550W with Active PFC & 2 x 12v rails. As I mentioned in my other post, AcBel is a good lower mid-range brand. Kingston is a good mid-range for RAM. Liteon is a good mid-range for DVD-R. Case is totally personal preference: just remember you get what you pay for. Cooler Master make some well-priced fairly well built cases that cool pretty well, but there's too many variables (like whether you plan to overclock, how much room is in your budget, what cooling your video card has, how warm an environment the case will sit in) to make any hard & fast recommendations. Even a "cheap & nasty" case will do the job: one can always add in a few case fans if needed.