Since we don't know the software you are using, or the precise type of programming you are doing, then I feel we should recommend the top. The very top. The tippy-tippy-top! Anything less would be a disservice to you and you could be frustrated with our recommendations and vow never to come back. We wouldn't want that now, would we?
1. Quad core or hex core i7. Maybe even consider a 2P board with two quad or hex core i7s. I mean...you did say "big data". What does that mean if it doesn't mean "BIG DATA"? Say it if you mean it. Pay it if you say it!
2. 32 GB RAM minimum. Again, you say you're doing "big things", so without knowing more detail, I feel obligated to suggest 64 GB to be safe. Some 2P server boards will support 128 GB...
3. HD 7970 GPU if you are an AMD fan or a Titan if you prefer Geforce. Any of those will drive two monitors and have some left over for GPU number crunching. You might even want to consider an HD 7990 like I am, because that would give you two GPUs, not so much for graphic work...but for the GPU number crunching that we don't know about.
4. Power Supply should be 800 to 1000 Watts, minimum.
5. You say your wife hates wires. But you cannot get away from wires completely. If you don't believe me, just look under your car's hood, or under your desk! Bluetooth sometimes has its own problems. I say embrace the wires. Learn to love the wires! Just do your best to hide them.
If you and your wife both hate music of
all kinds, then just get some cheapo crackerjack speakers, or better yet, just shut off the audio and focus on buying more CPU. But if either of you even remotely likes music (even if it's just your wedding song played on endless loop), then please spend some time on this purchase. Bad speakers are fatiguing to listen to, and you don't even know it! Good speakers will reduce subconscious fatigue and can be had for not that much money.