@bpeck - i was trying to send you a private msg to your question but am unable to. i'm going to try my best to help you out... and also, it's not alot of questions you're asking like the 'super user' claimed below... but i will try my best to answer them.
okay, here's the first thing... you're using an amp and unpowered speakers... there's 2 kinds of speakers - powered (which don't require an amp, they're just like plug n play. you plug them in, connect them to your mixer, and you're good to go.. i like powered speakers.. it keeps everything simple, and that's what i like - simplicity.). Then, there's what you got - unpowered speakers. Unpowered speakers tend to be cheaper then powered - understandably - i mean they're not powered. So what happens is, when you have a pair of unpowered speakers (such as what you got), you will need an amp. The amp is what is going to get the sound played thru your speakers (the unpowered ones).
So you're going to need to hook up the unpowered speakers to the amp. Now, i don't use this type setup, but when i use to play shows w/ bands in the past, since i didn't know how to connect my gear to theirs, i let the band handle connecting me to their amp... i think what they did was run my 1/4 inch jack (RCA i believe) - one end was in my master out part of my mixer (or line out), and the other ran to their amp. the amp ran to their speakers. don't quote me on if it's line out or master out... i can't remember it was a while ago.. but i know the band hooked me up. if i was you, i'd ask a local band to tell you the setup, they'll definitely know... or a music store who's well versed on the setup's - or a soundman.
but i know for unpowered speakers, you will need an amp. speakers go to amp, amp goes to mixer, mixer goes to turntables or whatever you're using for the instrument, be it midi controller, etc..
now here's the other part. you mentioned you're using traktor scratch duo 2 turntables - i use to own a mixtrack so i am kinda familiar with traktor (i hate it, lol)..
when working with traktor, you're most likely going to need a laptop or computer, since it's software. i am aware that this software comes with 2 vinyl records, so to me that reminds me of serato. i haven't used either, but i may be able to provide some guidance for you on it.. seen it used. i'd like to try at least serato.
if you have your sound setup like i mentioned above.. your mixer is going to connect to whatever you're using as the instrument.. now traktor scratch duo 2 is on the computer. if you're doing a hands on type thing w/ that program, then you're going to be on a midi controller. the midi controller will connect to your mixer - only if it has a soundcard in it (such as vestax typhoon having a built in card). however, if you are on something like mixtrack (not the pro version, the one that doesn't have a built in card), then you are going to need a card such as native instruments audio 2 dj or the other high end ones... now if you need something like that - setup will go something like this:
laptop to midi controller - to audio card - to mixer - to amp - to speakers
if the midi has a card in it - then setup goes something like this: laptop to midi controller - to mixer - to amp - to speakers
now if i was you and you want to simplify this crap, i'd sell your amp and your unpowered speakers or trade them in to a music store for POWERED speakers. get powered speakers - cuz with powered, you plug in the powered speakers. you rca your 1/4 inch cord from the speakers to your mixer. then your turntables go into the mixer.
or if you're using midi, i think nowadays since the midi's have built in soundcards and mixers, you could just plug your midi right into a powered speaker and go.. it really just depends on what you have. but if i was you, i'd sell the amp and unpowered speakers and go for powered. much easier and way less hassle.
hope that helps
