Old comps

As others have mentioned, unless you want to crunch CPU tasks only, the CPU is relatively unimportant for GPU crunching.  I take it that the example that you used

indicates that you are interested in GPU crunching?  If so, the following comments about giving new life to old hardware might be of use to you, since they are specifically aimed at upgrading with a productive GPU.

Before the advent of GPU crunching (around 2009), I built a number of hosts specifically for CPU crunching.  The CPUs involved were both dual and quad core, Q6600, Q8400, E6300 from Intel and a couple of Phenom II from AMD mainly for comparison purposes.  Intel tended to be more expensive to buy but much cheaper to run with significantly better output so I've tended to use Intel exclusively since then.  With the advent of Ryzen, that could easily change in future.

I still own all those old machines and around 2015 I was thinking about retiring them.  I had the opportunity to buy AMD HD7850 GPUs (Pitcairn series) at the time quite cheaply (basically the same GPU existed in the new R9 270 and old stock was being cleared).  I tried a couple and found how well they would perform in the hosts I was going to retire so I bought a bunch and upgraded instead :-).   They are all still running. I haven't had a single HD7850 failure in that time.

More recently (early this year) I brought some Q6600 based machines out of retirement (they were 2008 vintage) and upgraded them with RX 460 GPUs.  They produce pretty much the same as a HD7850 using quite a bit less power.  The ones I have don't need an external PCIe power connector.  As a result of this, I've bought more RX 460s and upgraded other 'close to retirement' hosts that had Q8400 and E6300 CPUs.  These do quite well power consumption wise because I only use 1 core for crunching CPU tasks.  They consume around ~160W at the wall crunching 2xGPU and 1xCPU tasks.  RAC (pretty much independent of CPU) is around 250-300K.  They run on 300W PSUs (rating is 270W on the 12V rail)

There are a couple of things that are very important to consider if you want to go the upgrade route.

1. Don't use the existing PSU in an older machine if it's not a modern design.  Avoid generic PSUs that are 3.3V and 5V 'heavy'.  You need a PSU that can supply pretty much its full rated power on the 12V rail.  Inspect older PSUs internally for swollen capacitors and non free spinning fans.  A 300W PSU should be OK for a RX 460 (or RX 560) GPU provided it can deliver at least 270W @ 12V.
2. If you need to upgrade the PSU, don't just accept the ratings as written on the label and don't buy some no-name cheapie.  Find the UL code on the label ('E' followed by six digits usually fine print and located near or under a rather large backwards 'R' merged with a 'U' to form a sort of sloping logo).  Google the code to find out who actually made the PSU.  Google the PSU model to find any reviews.  Don't buy a PSU that's not at least 80+ certified - perhaps at least 80+ gold.  If you plan to run the machine for more than a year or so, it's worth the extra.
3. You don't need a whole heap of RAM and faster RAM doesn't seem to make much difference.  I try to have 4GB in my older hosts - dual channel does seem to matter so 2x2GB rather than 1x4GB.  I have several running very well with 3GB (2GB + 1GB) without any noticeable ill effects (still reports in the BIOS as dual channel.  I even have a couple with 2x1GB that are still able to run 2xGPU and 1xCPU tasks without hitting the swap space whilst still running a full KDE desktop environment.  I'll get around to finding some more 2GB sticks one of these days :-).
4. Pay attention to case cooling.  Rather than adding/upgrading case fans, leave the sides off if possible.  That does a better job than case fans.  Also much easier to regularly inspect heat sink fins for buildup of dust and fluff.  Using a soft brush and/or compressed air, remove any accumulated debris.
5. Pay attention to motherboard capacitors.  Don't try to use any older machine that has obviously swollen capacitors on the motherboard.  It likely wont run under load for very long.  Motherboard capacitors are replaceable if you have a decent soldering iron and basic soldering skills.  You just need to find low ESR (preferably Japanese) caps with equivalent (or higher) voltage rating and about the same micro-farad rating.  Good brands are Panasonic, Rubycon, Nichicon, United Chemicon, for example.
6. When considering the purchase of an older machine, don't pay a premium for i7 or i5 and don't buy AMD.  I have tried an FX-6300 hex core and (even ignoring the extra power) it can't get the same output with the same GPU as a Pentium dual core or an i3.  And the power draw is higher too.

Sorry this has become so long.  Hopefully some of it might be of some use to you - or to any others who might be interested in exploring the same path.  I think GPU upgrades like this are a good way to increase output relatively cheaply.  Make sure it's a relatively modern GPU - RX 460/560 [not 550] can be found quite cheaply and perform really well.  I don't use nvidia - too expensive in my neck of the woods and older ones that are more affordable (like the 750Ti for example) produce less than half of what I can get from an RX 460 (RAC of 115K compared to 270K).