What parts do you have sitting in your closet that you might use for a new build?
Building it yourself is really not that hard if you follow the type of detailed instructions I linked above. I think paying someone $50 is a fair option - assuming you have someone really good to do it. Note however, that you will lose some of the advantage of building it yourself- and have no one but online forums to turn to if you later have problems.
Perhaps you could find some local group that helps people BYO - perhaps ask at local computer stores or google it with name of city. Or, for the same $50 maybe you could find someone not to build it but to help you build it - to provide direct guidance.
For the i7 mobo - are you looking for the new i7 Sandy Bridge processor with the 1155 CPU socket or the older i7 with the LGA 1366 socket?
At your budget level you should go for a 8GB of memory in the 2 x 4 GB configuration. With Windows 7 4 GB is considered the minimum level for memory and the 4 GB pairs don't cost that much. That assumes you have a 64 bit OS.
Sims 3 does not take a high powered video card - actually lower powered cards will work well. For good low end video cards, take a look at this site which has recommended models at different price levels:
Best Video Card Upgrades for Non-gaming Use
However at you budget level, I suggest getting a little better card such as:
Video card tests – for GTS 450 – Multimedia comparison
Compares 220, 240,9800,450, 460, HD 4770, 4850,5570,5670,5750,
Fermi Light: Nvidia GeForce GTS 450 Review . Page 5 - X-bit labs
Page 1 of review
Fermi Light: Nvidia GeForce GTS 450 Review . Page 9 - X-bit labs
GIGABYTE GeForce GTS 450 OC 1GB Video Card[IMG]file:///C:/Users/Rockland/AppData/Local/Temp/msohtmlclip1/01/clip_image001.gif[/IMG] - $110 AR
Newegg.com - GIGABYTE GV-N450OC-1GI GeForce GTS 450 (Fermi) 1GB 128-bit GDDR5 PCI Express 2.0 x16 HDCP Ready SLI Support Video Card
GIGABYTE GeForce GTS 450 OC 1GB Video Card :: TweakTown USA Edition
An SSD would be nice to have to speed up booting times, however it won't affect other performance much so I would get all the other necessities first and only ad the SSD if you have discretionary funds after that. Note that booting times won't even affect you much at all if you hardly ever turn off PC - I mostly use the sleep function and machine is ready to go when I start. I have Vista and the fetch functions makes most commonly used applications load quickly.