I recently built a new computer, here are the specs:
ASRock Z77 Po3
320GB Seagate Hard Drive
2 x 4GB Samsung DDR3 1600 RAM
I recently encountered about $100. Would it be better to buy a graphics card with it or an ssd. What would give me better performance overall and what would be better for games. Also, would an $100 graphic card be much better than the Intergrated graphics (Intel HD 4000 Graphics)?
Pretty much any $100.00 graphics card will improve the onboard graphics. Having a separate graphics card also takes a load off your CPU. However, that having been said an SSD will speed up the load time of your OS. I use 2 SSD, one for my OS and the updates for the OS and the other for my games. Personally I would go for the SSD and wait to save up more money for a quality graphics card. You have an Ivy Bridge processor and your board has a PCI-E 3.0 so if you save up your coin you can put one kick ass GPU in what you already have. Personally I would never go back to an HDD for my OS now that I have discovered the speed of a SSD. There, my official 2 cents worth.
"Also, would an $100 graphic card be much better than the Intergrated graphics (Intel HD 4000 Graphics)?"
like 1000x intergrated graphics is pants for anything other than MS Word.
Depends on what you're doing. Intel HD 4000 is respectable for most uses, but not really sufficient for a serious gamer. SSD's increase system responsiveness by quite a bit, and can cut down on power consumption (~6w), however they offer no real performance boost, just faster load times. A dedicated GPU would dramatically increase gaming performance, but personally, anything short of a 7770 isn't really worth it.
If you spend more time in games than surfing internets and other misc non-game activities, then pick up a GPU. Otherwise SSD.