New setup

I'd think one of the PC builders here on this site would be your first stop.  That price floats, depending upon what you want.  But at least you know you've got that part of deal done.
 
And are you sure you a mixer and a soundcard?  More bang for buck getting a muti ADDA interface.  Unless you need the external mixer.  Otherwise, you just plug into the interface and use the soft mixer to, well, mix.  Within your budget you could get a Focusrite 18i20 or 6i6, the Steinberg usb, Roland or such.  They are all about the same, quality wise. 
 
Cheap analog mixer?  There isn't that much difference, either, between competing units at the low end of the scale.  You could find a mixer that outputs digitial stereo via USB, which might make sense.  If I had to choose I'd go w/ Allen & Heath, since I've used other stuff of theirs and it was good. 
 
Or just keep the behringer and go a step up by buying the focusrite Forte interface, or RME baby face.  That way you won't have to worry about "upgrading" your interface ADDA anytime soon.
 
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Glad that helped.  An analog mixer is nice to have.  It makes it easier to do headphone mixes and makes a darn good patchbay as your system grows.  But for just choosing synths etc. that are plugged in, it really ain't necessary since you can choose that input up in your soft mixer.
 
Something like the Forte or Babyface mentioned above is a good, long term investment.  The idea is to get enough quality you won't feel the need to replace it in a year or two, whether for outboard or the computer itself.  The Forte has 4 ins (2 mic preamps, two lines), which is flexible enough for small studios, and the preamps should be better than your mixer's so you can use them directly and plug in instruments into your behringer mixer to choose which instruments to send for recording instead of having to patch.  I prefer at least 4 outputs - one to montior and the other for outboard effects and such.  The Forte has a hands on knob like my TC Konnekt 48 remote. 
 
While a custom built computer is great and can save a lot of time and headscrathing, a well-choosen Sony or HP (I've used both) works great too.  They do put a lot of extraneous software on those, but that is not the killer it used to be w/ single core, memory-light slower computers.  Something else to think about.
 
research before you start throwing money out there.  Understanding how and what you want to record is the first thing, then the hardware to make it happen.  A few days or weeks can make your money work for you.  Figure out how much you can spend, and get the best quality hardware you can afford.  Don't be afraid to skimp on one part to get good on the others, as long as you realize you'll probably need to upgrade later as soon as you get the money.  There isn't usually a night-and-day difference (say, between the forte and and the forusrite scarlet line) but if you stick w/ recording you'll end up wanting a better preamp, etc.  That is natural growth - or greed.
 
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