Borsch is pretty much correct, FSX is an old 32bit simulator software with many issues and problems. That said, once you do master the ins & outs of FSX, there is plenty that can be enjoyed & learned from it, depending on what you are after of course.
There are many thread/posts on many forums (check AVSIM hardware forums or google search on fsx hardware), inc here
http://forums.overclockers.co.uk/showthread.php?t=18172358 that will give you hardware advice.
My advice in short:
CPU: Get the best stable OC CPU you can buy, could stick with value for money in the i5/i7 range but I recommend at least quad core as you might need the extra cores/horsepower for any other programs you may decide to run along side FSX which can be shoved on other cores, so perhaps even look at a fast running six core, if your budget allows it.
GFX: Depending on the resolution you going to be running FSX at, if anything of 1920x1200 or below, stick with a single decent Nvidia 500 range card, with at least 1Gb of Vram (useful when you start having lots of HD textures in FSX). If you planning to run higher res on either single monitor or multi-monitor, then perhaps a SLI option is worth thinking about (not that FSX takes any advantage of SLI but higher resolutions/multi monitor eats up Vram quickly so having 2x 1GB Vram cards is handy). Again, you could go for value for money and get 2 cheap Nvidia 500 range cards, or perhaps get a single 580 or 680 with 3Gb/4Gb of Vram.
HD:
Get a fast small SSD drive for OS, get a decent sized SSD for FSX (I recently purchased a Crucial M4 512GB but using it on SATA2 atm till I can afford a major upgrade in both CPU & M/B and hit SATA3 but in the meantime, I have FSX already build on it). You could also choose a cheaper option and still fast by getting 2 or more fast HDs raided for FSX, there are some 10000rpm drives about which go pretty fast when raided. Still SSD is getting cheaper now and is simply faster then mechanical drives.
OS: Definitely a 64 Bit OS, again FSX is 32bit program but other addons/programs you might decide to run along side FSX may utilize a 64bit environment better, besides it better using your memory above 3Gb, FSX won't but other program most likely will.
RAM: at least 6Gb+ but no need for massive RAM as that will reduce your OC potential on your CPU, sweet spot is usually 6-8Gb.
Controller: Find a joystick with both thrust and rudder control, again, no need for expensive stuff unless you have the budget and you really need it.
Most important advice: DO NOT throw money into the wind. Because FSX can turn into a very expensive hobby both on hardware & software front. Best thing to do is start with a decent but good value for money custom build PC with room to expand in the future. Once you really feel the flight sim bug bite you, then you can always start throwing more money into it for either hardware or some nice aircraft/scenery/util addon.
That is my advice, in short, sorta...
Good luck.