ASG,
I think you are confusing things. The computer runs handles digital effects, spooling audio and everything else inside the box. It receives timing info from the interface. Interface usually means a combination unit of converters w/ a clock, maybe preamps and definitely a means of digital outputting to the computer.
Your saffire includes all three of the above items. The audio comes in and is converted (and the clock makes sure all the digital bits are lined up). If you use a mic the preamp converts a mic level electrical signal to a line level signal so the saffire can "hear" it. It uses USB to send the digital bits (lined up correctly) to the computer so your DAW can manipulate it in the box. And then the manipulated signal goes back out to the saffire, is converted to analog and on out to your speakers. THe computer and the interface are two separate entities, tho not closed. You upgrade the computer for more realtime manipulation (we used to have to do anything cpu intensive off-line). 96 k recordings do twice as much computation as 44.1. While the interface simply turns the digital ones/twos from the computer into audio.
Some "interfaces" are merely converters (w/ the attendant clock). Like the Lynx Aurora. It is a separate rack unit w/ converters in it and a card for outputting the digital info. It can be AES but your computer needs a card to plug those cables into (and Lynx makes a good one). Or it can output over FireWire or USB. It does one thing and one thing only - convert analog to digital and send the digital out. You would need a separate preamp to record a mic well (at most you would get a weak signal from a dynamic).
A faster computer will let you manipulate higher rates and pile on more effects in real time. A better interface/converter would provide (hopefully) better ADDA conversion, but most of us agree your bang for buck on the purchase would be small. Unless you go to the very high end like Burl or Prism etc, and then you need a very good system to get the most of it (monitors, outboard etc.).
From what you described, if I was you I would make sure that I do hear the difference between 44.1 and 96 by blind testing. If you can hear the difference 70-80% of the time, get a new computer to run the higher rate first. If not and the saffire meets your needs now (number of inputs etc.) I would invest money in a mic, or room treatment, or a preamp before I upgraded the converters. But remember, it is a system. It makes no sense to convert audio that you can't hear because your speakers aren't good enough to show the difference or your room has big flaws. But as you work on the technical side and your ears get more experienced and your mic placement technique gets better, you will learn where the flaws are in your system and be able to improve those. A consistent upgrading in step w/ your audio education is the way to go, along w/ buying the best equipment you can so you aren't throwing it out the next year as you graduate from good sound to great.
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