What is the best GPU for deep learning currently available, and additionally - what might be considered a good machine for data-intensive computing, in terms of processor parameters, RAM etc. ?
The CPU probably isn't quite so important if you have a good GPU, since the GPU is going to be doing most of the heavy lifting. I ended up getting the Intel core i7.
The amount of RAM you need again depends on your application and the size of your datasets. More is better, but costs money.
Seeing as you specifically asked about GPUs (not ASICs/TPUs etc.) and cost and scaling aren't part of the issue, then, for a single 'unit,' you can't really go past NVIDIA's DGX-1 system:
It's 8 Tesla P100 GPGPU units (i.e. modern awesome GPUs) tightly bound via a NVLINK high-speed interconnect and managed by dual 20-core Xeon E5-2698s, with a 8 TB SSD (in RAID0 configuration, generally resulting in much higher read performance). The interconnect is very important, as I/O is most often a bottleneck, depending on your application.
Note that the benchmarks given in the (nice) comparison by Tim Dettmers notably do not include the more performant Tesla P100 cards, which the DGX-1 is based on. But some good points are made about bandwidth and cost.
However, this is all without knowing what your application is. If scaling is likely to be an issue and your peak load is going to be one-off, then a cloud solution such as AWS (an EC2 P2 instance: https://aws.amazon.com/ec2/instance-types/ ) might serve you better.