Well you are right in your post.But i guess you need to tell us what is your budget.
To be honest if you build your machine it will be less expensive.Now do you know how to?
If you go ask to a shop they will try to give you what THEY want.
From yor specs.Well they are low.Memory its ok if you want FS9.Processor needs to go a bit faster.Graphic card....well nop.But like i said all depends in your budget and what you want from FS.We know money its short.If i was in your skin i would look something on ebay, sometimes you can find good deals.But we need to know "how much".We can talk about specs all evening, but the money you have its what it will say the rules.

Ok $600.
Well first you need to know what MB you have, to see if you can go with another processor.You can find faster AMD for less than $100.Then, and thinking that your MB can accept PCI-Exp. you can find a good card with 512megs between $80 and $150 (so $250 so far).Then we need to see your PSU (you can find a 650w for $80).Now ,and still thinking that your MB cames with PCI-exp and is not very old, we need to see memory.(so far we are on the $320 - + for budget)What kind of ram you have? DDR, DDR2 ? If not you can buy like 4gb for $60 ($380).IF all this cant go with your MB, then you need an MB, and one for $150 its already a good one ($530), maybe we can cut MB price depending in what you have and what you need.
Let me remind you that this upgrade will be ok for FS9, but medium FSX.
But i can also tell you that with $600 we can go many ways, to build a good and ACTUAL (if there is any) machine.
Keep us posted, you will be fine.

PS - Welcome to "HEL" of pc's 

This is an example (i would still change the video card and be in budget) and some of those will hold FSX pretty well

http://cgi.ebay.com/INTEL-E7600-3-0GHz-DUAL-CORE-CUSTOM-COMPUTER-SYSTEM-NEW_W0QQ...

or
http://cgi.ebay.com/AMD-Phenom-9650-QUAD-CORE-CPU-ASUS-M3A78-CM-4GB-kit_W0QQitem...

and still with $ for a good video card

In Belgium try those

http://cgi.befr.ebay.be/PC-NOUVEAU-AMD-X2-245-TOUTES-APPLICATIONS-ET-JOUEURS_W0Q...

Still money for video card

This one is ok

http://cgi.befr.ebay.be/PC-Gamer-Intel-E6300-4Gb-500Gb-Nvidia-9600GT-1gb_W0QQite...

OR

http://cgi.befr.ebay.be/NEUF-PC-EVOLUTION-AMD-ATLHON-64-X2-6Ghz-2Go-250Gb_W0QQit...