The Gateway of Sound
It is the gateway of sound in and out of your computer. It transfers the signals of your instruments and microphones to your computer and plays back audio coming from the computer.
You need to consider sound quality, responsiveness (low latency) and the amount of inputs best for you.
PCI, FireWire or USB
There are several ways to connect an audio interface to your computer. The usual suspects are involved here like USB, PCI or FireWire. They differ in bus-technology and transfer speed. The faster the better is the golden rule here. You have to decide which one you want to use before you buy an audio interface for that connection. Audio interfaces usually support only one technology.
I decided to go with an USB 3.0 audio interface. With 625 MB/s, USB 3.0 is one of the fastest these days. Also, USB 3 connections are usually available in any computer and the price range of USB 3 audio interfaces was friendly to my budget.
Why is transfer speed important?
The keyword is "latency". Latency describes the time it takes for audio signals to travel from the outside world into your computer. And that route leads through your audio interface. The audio interface also does things to the signal, it digitalizes it so the computer understands it. You also want the signals to be fluent and not stop or drop inbetween. You also want to hear what you play while you play it back through the audio interface. The connection speed of your audio interface is one factor that helps to keep the latencey low.
How Many Inputs
This depends on how many inputs you want to record at the same time. The smallest audio interfaces have two inputs, e.g. to pick up a guitar and one microphone. That is usually enough if you do all your recordings alone and each track separately. That's what I usually do but I also have use cases where a friend stops by to record a song live with two guitars and microphones. That requires four inputs already.
A secondary factor in my case was that I had ordered the Zaor Miza 88XL studio desk coming with 19" rack space. Audio interfaces for those usually come with 8 inputs.
I looked for 8-input USB 3.0 audio interfaces that are 19" rack mountable. Since I have no practical experience I went by customer reviews and selected the ZOOM UAC-8 that I felt had one of the best reputations. For about 600 € it was also at the lower price range in its class.