Do I need a DAC and how much should I spend?

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Sorry for the ultra basic question here. I tried searching and the search function won't allow words like need, what, should. So I'm at a loss and imagine (hoping, haha) lots of other folks are too.

I'm building a simple system for my family room that will include a couple of the 3116tpa D chip amps, and a pair of speakers that are 1/2 way decent. Event 20/20 passive monitors.
I will probably throw a little bear tube pre amp in there unless it's suggested not to. It will all be played through a dedicated ipod with flac files or my iphone streaming spotify at 320k.

From what I read, a DAC will improve the sound dramatically? How much do I need to spend to get a noticeable improvement? What kind of info do I need to be armed with to get the right one for me? I'm assuming it needs a RCA in. Outside of that I'm pretty much lost. I don't even know where it would go in the line?
Ipod<DAC<pre amp<amps?
In which case it would need rca in and rca out

Lastly as I'm building a case for the amp I would prefer it be a complete board (no case) that needs no or very little tweaking. But if it comes in a case that is fine too. I'd like the to keep the cost (well) below $100 if possible. But I'm open to having to spend more if I need to.
 
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