4K gaming would make the build pricey as you would ideally pair it with a GTX 1080ti - but GTX 1070s are at an insane price at the moment making the 1080s look relatively good value...
Also, i'm a fan of single card solutions to a PC - and although the 1080ti does the job at 4K it's not as accomplished as GTX 1080 at 1440p - which still looks amazing. Something to consider as would bring build costs down and perhaps stop the thought of SLI at a later date - which i'm personally not a fan of (but i've been out of 'that' loop for a while).
For gaming purposes and a multi table poker the 1600X would suffice - but you could choose to go the extra and get the Ryzen 7 1700/X, but wouldn't be totally necessary. Unless you plan on gaming and playing poker at the same time? But suspect your playing style would come across as 'Maniac' doing this - which may or may not aid you depending on how much you did it. Certainly the unpredictability of your playing style may help if you didn't do it all the time.
Monitor wise you would need to make the decision whether a large 16:9 monitor would suffice (or even a couple) or whether you want an Ultrawide. I'm not a fan of ultrawides as you have to move your head when you game - but you may actually benefit from this type of setup for your needs - gaming aside). Coupled with this decision is whether G-sync is important to you - or more importantly whether you're prepared to suck up the cost as it will add considerably more to the price of the monitor in comparison to a reasonable IPS panel at 60Hz.
If you can answer the above and give me an approximate budget i'll cobble together a few example builds for you. If you have further questions after that you will be best served making a dedicated thread as this is Beady's thread - and things may get a little confusing.
You're looking at £1600 - £2500 for the computer for 4K gaming (depending on CPU and future MB and PSU use) and then adding an additional £500 to £1000 for the monitor, depending on what you want.
Basically you could do a build for as little as ~£2300 all-in for a single card solution and standard IPS large 4K monitor. However, if you start to factor in future SLI, a 1700X and a large Gsync/ultrawide then you start approaching £3000 - £3500.
Decisions...