If you both read the 3rd line of the cmd, you can see it's have difficulty connecting to the pool. It's most likely nothing wrong your end, but pool end.
I've been hitting the same message for ages, unfortunately giving up on DOGE now and continuing to mine Litecoins as they at least provide me a break even (Taking into account electrical costs, internet and pool uptimes )

Here's your answer from me doing a quick test:

1; There are various statistics and information out there for every computer component, if you want to check the entire usage of your own computer, yourself and to a precise value you can get yourself one of these; Kill A Watt / Amazon
Otherwise, a quick google search or trawl of a reputable forum such as http://overclock.net will reveal the right range of Wattages for your components.

2; I doubt that Nvidia card runs at 500W, that's just the recommended minimum power supply Wattage for the card. From what I can see and attain, the NVIDA GTX 650 Ti BOOST runs a maximum load wattage of around 240-250W.
The minimum recommended is usually a good guideline of the overall sort of powersupply your computer should have. The 500W is to allow for CPU/HDDs/Fans/etc on top of the GPU load Wattage.

In terms of compatibility, you needn't worry. If your Motherboard has a PCIe x16 slot (Which it clearly has for your 650 Ti) then ANY PCIe device (GPU/RAID card/Sound card/etc) will work.
The restriction is on the software and drivers to the Operating System, not the Hardware itself. And given how ALL modern GPUs have support in Windows, I doubt you'll ever expect an issue.
Just remember to download and install the correct software package/drivers for whichever GPUs you use;
ATI/AMD: http://support.amd.com/en-us/download
Nvidia: http://www.nvidia.co.uk/Download/index.aspx

3; There's no real rule of thumb, higher shader count and faster clock speeds are usually your best bet. But try to buy cards in newer generations, as they're more optimized each time. A HD 79XX card is the most advised 'mining' card, or some of these newer 280X / 290X GPUs are equally as good if not better. Just check the Litecoin Hardware Comparison sheet and (as a rough guide) change KH to MH when doing SHA-256 (Bitcoin) instead of Scrypt (Litecoin/Most Altcoins)
SHA-256 seems to benefit from higher core speeds whereas Scrypt benefits more from higher memory speeds.
https://litecoin.info/Mining_hardware_comparison

4; The Identifiers are usually easily looked up from the Manufacturers site, or using general shopping sites;
I.e. A 11196-00-20G is a Sapphire 7950 3GB as Google reveals;
http://www.sapphiretech.com/presentation/product/?cid=1&gid=3&sgid=1157&pid=1439&psn=000101
http://www.amazon.co.uk/Sapphire-11196-00-20G-HD7950-GDDR5-Graphics/dp/B0091MER16


Hope this helps ^_^

Seems like the pool is hit and miss for me too;

C:\Users\Iselia>paping doge.scryptpools.com -p 3333
paping v1.5.5 - Copyright (c) 2011 Mike Lovell

Connecting to dc-2890f79c.scryptpools.com [162.243.64.168] on TCP 3333:
Connection statistics:
        Attempted = 83, Connected = 27, Failed = 56 (67.47%)
Approximate connection times:
        Minimum = 0.00ms, Maximum = 127.53ms, Average = 30.93ms

Not a very promising result. x-x;

Headroom: As in the sense of having enough available wattage/power on the PSU to power multiple GPUs or whichever GPU you pick.
I.e. you need roughly 300W load to mine a 7950/70.
So if you have a 500W PSU, subtract (generous figure, but I'm allowing for discrepancies and degradation in PSU) 10% (50W) leaving you with 450Ws of usable 'headroom'.
Take out 300W for GPU, leaving 150W
Which leaves 150W for your CPU/RAM/Fans/HDDs/etc.

And costs if we assume, substitute in your own values if you know them,
Electrical cost per KW unit: $0.20
800W PSU (If we assume it to be 100% efficient at 100% load (which is basically impossible)) 800W = 0.8KWh (Kilawatt Hour)
Hours in a day: 24 Hours
Do some simple multiplication
$0.20 * (0.8 * 24) = $3.84
Price per unit multiplied by (KWH of device multiplied by 24 hours in a day)

Take into account that's "roughly" 70Khash too and if NO electrical OR internet fees were incurred;
He could get around: ~$0.40 worth of BTC/day or $0.50 worth of LTC/day

It's not ground shaking or earth moving, but it is something.

I've tried to look for PCIe x1 GPUs for quite awhile, just something basic that I could shove into an old server and give me a few more display choices (onboard of one server is a little trippy) and not had much luck.

As correctly stated earlier in this thread, there will be no difference in hashrates as the bandwidth of a PCIe x1 slot is more than enough, using PCIe x1 extenders to fit PCIe x16 GPUs works perfectly fine (tried and tested myself)

Cost effective wise, if you're going to use Nvidia cards then don't attempt to mine SHA-256 coins, or even Scrypt coins above a difficulty of like 30 as your hashrates to earnings are almost likely going to be negative if factoring in Electrical and Internet costs.
If, however, you're on a flat rate tariff, whereby you pay a single rate for your electric and it doesn't increase, then mining any GPU (As long as you break even) would be well worth it on any coin.

If you feel daring, or just want to test the water per say. Pickup some of these newer coins floating around, 'funcoin' or not just see how things play out for a bit and see if you want to continue mining seriously.

EDIT:

There's no reason why that motherboard/computer cannot support an ATI card. Such person who told you otherwise either doesn't know what they're talking about or are heavily biased to certain setups and manufacturers.

As long as you have the headroom and ability to power the graphics card from your PSU, you'll be fine.