hissing noise/static from speakers and headphones... Need external DAC/sound card

Just to clarify, the hissing noise only began after you installed the new graphics card? Also has anything changed about your setup be the graphics card. On to your questions.

1. Some people find SPDIF to sound a bit cleaner sounding than USB (assuming the same DAC), but these are people with really revealing speakers or headphones along with an appropriate amp and have really good hearing. Most USB DACs are also USB powered, so sometimes the dirty power can cause some audible differences. However, sometimes a USB implementation is superior to the SPDIF and vice versa. So in short it's is not going to make a difference and even if it does you probably won't care.

2. As for recommendations, I've got plenty of them being an audiophile. It really depends on your budget and what features you want i.e support for decoding higher resolution audio. DACs range from $20 to $20000+. When you pick a DAC you get diminishing returns as you go up in price. So let's start with some recommendations.

HifimeDIY Sabre U2
http://hifimediy.com/DACs/ready-made-dacs/U2-DAC
This is one of my personal favorite budget picks. It's small and unobtrusive, but more importantly it sounds good and it just works.

Geek Out by LH Labs
http://marketplace.lhlabs.com/collections/all
I'm just gonna send you to their product page. There's the original Geek Out that comes in three varieties. 100, 450, and 1000. The numbers refer to the power of the headphone amp in mW. The 1000 sounds the best used as a DAC. However the differences are minimal. They are also about to release V2, which in theory should be better in every way.

There's also a couple of products from Fiio, which is brand that is considered one of the best values in the audiophile world. Just go on amazon and type in "Fiio dac".

I'm gonna stop before this post gets too long as I could go on for hours about different audio products. Set a budget and I can give more recommendations.

Line out is generally better for connecting to a speaker (actually amp). A headphone out has the audio signal go through the headphone amp portion of the circuit in the Geek Out above and other DAC/Amps. More commonly it means that it is a port with low output impedance. Headphone outs are designed to drive the lower impedances of a headphone, which generally range from 16-600 ohms. Line outs have very high output impedance 10k+ ohms and are designed for connection to an amplifier, which also have high impedances. Impedance matching is important so that there is no excessive current draw that could damage a component. It is also so that the voltage(signal) is changed only where you want it to change i.e by the amp. Also a lot of line outs have a fixed level that is usually around 2.0V. Damage by current is rare as many electronics have fuses for the very situation. In short, follow what it says uses headphone outs for headphones and line out to connect to an amp. However in a pinch you are very unlikely to cause any damage.

In the case of the Geek Out one of the outputs is 47 ohms, which is acceptable for use as a line out. It's not ideal, but it does work and sounds very good. What you have to do is set the volume to max or some people say 99% on you computer. Then use the volume control on your klipsch to change volume. If you are using headphones you can plug straight in to the Geek Out and use the volume control on you computer. It will make your headphones sound better if they are decent headphones or it will make them sound worse if your headphones aren;t very good. I recommended that product because at that price it's performance and feature set are very good.

The Fiio D03K is a good product. It cheap and sounds pretty good. The cables can get kind of messy though. It takes a mini usb for power, needs a toslink or optical for the input signal, and needs a 3.5 mm or RCA for output. Not a big deal though, but sometimes cable clutter bothers people. As you step up through the food chain of DACs and Amps and really anything audio related you get diminishing returns. I do see benefit of maybe spending up to around $300, but the D03K would be enough for most people. Best part is that if it isn't to your liking you're only out $30. You can sell the fiio, give it to someone, etc and then get something else for yourself.

Here are two more options that are also very good. Both are under $100. Good performance an great value. They're also made in the USA if that is a factor to you.
http://schiit.com/products/fulla
http://schiit.com/products/modi-2