How can I achieve higher quality results from my bargain based 4K monitor? I just got the latest 2013 15.4-inch MBP 2.6GHz and I also have the 39-inch Seiki 4K television. 

I previously had a 2010 MBP 15.4-inch 2.53GHz and used a Mini-HDMI to connect to the 4K which was able to support 1920 x 1080p at 30Hz and 3840 by 2160p at 24Hz. 4K videos on Youtube had a picture that looked fantastic, but the 24Hz really put my ongoing enthusiasm in a bind.

Since I've upgraded to the latest MBP, which is in every way superior to my old build, how can I best utilize the new features and power to get the most out of the 4K or at least improve the 24Hz rate.

Are there any best practices to follow for movies, audio, browsing etc when you have a choice between Thunderbolt2, USB3.0, HDMI, etc? Are the dual graphics enough to push 4K at a rate above 24Hz? 

Perhaps there is a single cable that can solve all my problems.
Here is some information:

Apple lists the 2013 MacBook Pro with Intel Iris Technology as being able to run a 4K display at 4096-by-2160 resolution and 24 Hz as well as 3840-by-2160 displays at 30 Hz over its HDMI port. 

The latter is the resolution of the Seiki and conveniently as high as it goes at 4K – HDMI 1.4 is limited at these rates. 

Some manufacturers say that they will update their HDMI 1.4 to 2.0 which can do higher frame rates, but Seiki has made no such promise.