It appears that your board has a PCIx 3.0 slot. So, yes, you can add an NVidia or AMD/ATI card, provided that slot is not occupied, and your power supply has the appropriate connectors and can supply the needed power. It probably will, provided you do not go for a card that requires a lot of power and additional connectors.
The cost for those cards vary, but there are plenty in the price range you want. Be aware that the insertion of an add-on graphics may disable your onboard Intel graphics.
It is very likely that you just need to get a graphics card and that your power supply already has the necessary connectors. Unless you go for a card that is more power hungry, you should be ok.
Now, this is my personal position. I like cards with the NVidia chipset. Some like cards with the ATI chipset. There are many manufacturers providing these cards. Try searching a site like www.newegg.com for a card. You can select the features you want from NVidia and ATI based cards. One thing to watch - your case may not provide sufficient space for a full length card. So, be careful. It also would not hurt for you to open the case (with the system off and power unplugged) to see what space you do have, and what connectors you have on the power supply. I suspect you will be getting a shorter card. Another thing to watch - see if your available space will allow for a double width card or not. If it is a double width card, you need to make certain that there is nothing in the slot next to the PCIx 3.0 slot.
Once the card is plugged in, reassemble the machine, connect your monitor, and apply power. Third thing to watch - make sure the card provides the necessary connectors on the back. You will likely have no problem.
You machine should boot and you should see the boot screen on your monitor.
Now, I always go straight to NVidia for the latest driver. You may want to do the same. No matter what brand of card you get (ASUS, EVGA, etc), you can always get the latest driver directly from NVidia or ATI.
Just take it nice and easy with disassembly, power, card insertion, cabling, etc. If you have any questions, just ask.
Good luck and report back.