will this rig play ultra

Edit in response to question edit:

2: The first one is significantly better, though you could likely still do better for the money.

3: The first might be able to max some games, but the 660 Ti isn't a massively impressive GPU. The second definitely won't.

4: I am uncertain as to the requirements of 2k14, so it's a possibility, but the second has very weak specs and the first isn't great. However, if 2k14 isn't massively demanding, the first build might be able to max it out.

Those machines are so polar apart as far as budget i don't know why you would even compare them, of course the top build will be faster lol.

Hoo boy. Craigslist is about the last place I'd go for a PC, and I say that as someone who's sold PCs on Craigslist. Pretty much all the sellers are going to assume that you have no knowledge of PCs, and use that to get more money than the system is worth from you.
I can most certainly design a rig in the price range, but first I'd need to know a few things:
1: Where are you purchasing? (Country and state/province)
2: Do you need an OS?
3: Do you need a monitor or peripherals?

Wow, that's a really reasonable deal, actually. A bit suspiciously so, really. Make absolutely sure that this thing is fully functional before you purchase it. However, if it is, it's a fine system. Only thing I would drop (and drop with all possible speed) would be the PSU.

Figurative indication that you should remove and replace that PSU quickly. Apevia is definitely not a brand you want on your PSU. XFX or SeaSonic would be most ideal. Changing the PSU shouldn't impact performance in either direction, but it will decrease likelihood of an explosion.

Ah, Cyberpower. Almost certainly not, no. If it's between an online assembler and doing it yourself, doing it yourself is always more efficient. Looks like we're back where we started. So, just to confirm, $700, must include OS and keyboard?

Ah, Cyberpower. Almost certainly not, no. If it's between an online assembler and doing it yourself, doing it yourself is always more efficient. Looks like we're back where we started. So, just to confirm, $700, must include OS and keyboard?

Alternative AMD build:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($119.99 @ Newegg)
Motherboard: ASRock 970 Extreme3 R2.0 ATX AM3+ Motherboard ($92.55 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.98 @ NCIX US)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($69.99 @ Newegg)
Video Card: Sapphire Radeon HD 7950 3GB Video Card ($199.99 @ Newegg)
Case: Rosewill Galaxy-03 ATX Mid Tower Case ($42.50 @ Newegg)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($44.99 @ NCIX US)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Total: $682.46
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-12 18:00 EDT-0400)

It's a bit unbalanced (the GPU is stronger than what I would usually pair with a 6300), but it's pretty reasonable gaming system. Should be around budget with a decent keyboard if you can install OS without purchasing an optical drive, or a bit over (around the price of cars' build) if not.

Alright, I'll mock a new build up, and explain it in more detail.
To address the YouTube bit, some are, some aren't. I make some videos like that, and they're generally accurate to the best of my experience and knowledge. However, as with all things, some people who lack experience and expertise still want to put in their two bits, even if they're only misleading people.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3350P 3.1GHz Quad-Core Processor ($179.99 @ Newegg)
Motherboard: ASRock H77 Pro4/MVP ATX LGA1155 Motherboard ($82.55 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.98 @ NCIX US)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($69.99 @ Newegg)
Video Card: Asus GeForce GTX 670 2GB Video Card ($247.55 @ Newegg)
Case: Rosewill Galaxy-02 ATX Mid Tower Case ($39.99 @ Newegg)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($44.99 @ NCIX US)
Optical Drive: Lite-On iHAS124-04 DVD/CD Writer ($17.99 @ Newegg)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ Outlet PC)
Keyboard: Microsoft SIDEWINDER X4 Wired Gaming Keyboard ($49.99 @ Newegg)
Mouse: Razer DeathAdder 2013 Wired Optical Mouse ($59.98 @ SuperBiiz)
Total: $914.98
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-09-13 10:16 EDT-0400)

Here's what I'd pitch, for that budget. Now, from the top:
Intel i5-3350p: An Intel i5 processor, which is generally considered to be the most optimal option for gaming systems at current. Games presently favour quadcore processors, and Intel's quad cores are strongest. The 3350p is a pretty run-of-the-mill i5, but it does its job well.
ASRock H77 Pro4/MVP motherboard: ASRock is a well-known and well-respected brand for motherboards, and generally have the best price efficiency of all the major brands. The H77 Pro4 cannot overclock, but neither can the 3350p, and the loss of overclocking saves you about $120 between processor, motherboard, and CPU cooling.
G.Skill Ripjawes X RAM: G.Skill is an extremely solid brand of memory, which I use in my machine as well as most of the systems I have built for others. I used 8GB in this build because it's generally agreed to be the most optimal amount, though in a pinch 4GB is viable. This memory is clocked at an absolutely standard 1600mhz, which is about as much as you'll get a benefit from anyway.
Seagate Barracuda 1TB HDD: Seagate, like G.Skill, is an extremely solid brand. I use four of their HDDs myself, and have never had cause to complain. Though you could technically get more storage, one terrabyte is enough for most people, and if you need more storage later, it is quite easy to add.
ASUS GeForce GTX 670 Graphics Card: ASUS is one of the strongest brands in the business when it comes to graphics cards. Their DirectCUII cooler is quiet and effective, and they have reasonable (though not amazing) factory overclocks on their cards. Though the GTX670 is a last-generation card, that one is currently on sale for less than the GTX760, which it slightly outperforms. The 670 is generally good for high-max settings on all current games, though if you were looking for a bit more performance, there's a Gigabyte (also a very respected brand, and with a tendency towards excellent factory overclocks) 7970 available for about $35 more (http://www.newegg.com/Product/Product.aspx?Item=N82E16814125413&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=).
Rosewill Galaxy-02 ATX Mid Tower Case: The Galaxy-02 is a cheap and cheerful mid tower which was recently released by Rosewill. There's nothing particularly special about it, but it has a combo with Seagate's Barracuda hared drives on Newegg which makes it one of the cheapest cases on the market at the moment. As an added bonus, it comes with an LED fan, making look a good bit better than most >$20 cases.
XFX 550w PRO550W Core Edition Power Supply: XFX is a quite solid brand for PSUs, due to having all their power supplies made by the famed SeaSonic, who are generally regarded as the most reliable in the business. 550w should be absolutely fine for the system, whether or not you go with the 7970. You might want a bit more for an overclocking-centric rig, but with a non-overclockable processor, this is completely solid.
Lite-On iHAS124-04 Optical Drive: Not especially much to say about this. It's an optical drive which will allow you to install your OS, put in CDs, and otherwise use it as you would any other optical drive. Lite-On is an alright brand, and I use a very similar Lite-On drive in my own system. Due to a combo with the processor, this one only costs $10, which is why I chose it.
Microsoft Windows 7 Home Premium SP1 (OEM): It's Windows 7. Pretty sure you're already aware of this.
Microsoft Sidewinder x4 Wired Gaming Keyboard and Razer DeathAdder 2013 Wired Optical Gaming Mouse: These are a pair of fairly standard gaming peripherals. I specifically chose them because I use them myself, but I would suggest trying out peripherals with your own hands and seeing what works for you before you buy. I included these as a price reference.