A/D converters are very important..think of them as a very important gateway into your computer which can mean the difference between a crappy or accurate representation of your recorded sound. a good set of converters will stay true to your recording so, in essence, if you have the best amp, mic and guitars fronting a performance all of those won't matter if your converters are not good. now, prioritizing converters depend on your purpose for making music. mixing, recording and whatever else you plan to do really doesn't matter because, in the end, they all do the same thing..they convert signals from analog to digital (and vice versa) depending on what you are doing for a given production task.
good interfaces usually have good converters and all companies have their own champions and critics. listen around and do your research to find out which fits your budget. for more serious production places, a standalone converter is usually employed to take advantage of a company's specialization in making master clocks and converter machinery. Lucid, Mytek, Apogee, Lynx and a few other companies specialize in making converters and a lot of companies use their products. if you use a dedicated suite like ProTools HD, you may not need to use a standalone converter because their stuff is pretty good but some people I know still pipe to an Apogee even though they use a full-on HD system. different strokes for different folks, is what I say.
if you are a newbie, try looking into a nice interface first. it doesn't make sense having converters if you don't even know what they are because that is an investment that will require other expensive purchases such as a master clock, for one thing.
in my studio, i use both standalone (Apogee/ Mytek/ Aardvark OCX) and in-system converters (PTHD) so i can help you where I can. other experienced folks on here have a wealth of info and I'd pick their brains about their rich experience as well.
oh yeah...AD converters are not the same as an audio interface. an audio interface HAS AD converters in it but both are distinct from each other.