Industrially, copper is electro-won using lead-calcium-tin anodes and stainless steel cathodes. For ultra-high purity copper production, it may be electro-refined using high purity copper starter sheets as cathodes.
The last time I was at KUCC was in 2006, and they were using stainless steel cathodes. Everyone experiments with titanium and other exotic cathode materials, but the reality is that when you have 20,000 or 50,000 cathodes, you simply cannot afford titanium. A good commercial grade of stainless (I pick 316L) in a well-maintained cell (no shorts, good current distribution) will last probably 5-7 years. It is also available for every home-based user.
For home use you would have a difficult time with lead-calcium-tin, as it is impossible to make without some high tech equipment. The calcium is actually mechanically alloyed, and the sheets are cold-rolled. Calcium doesn't dissolve in lead, and in a melt the calcium just scavenges oxygen and becomes nasty calcium oxide inclusions that make the sheet brittle. I would suggest lead-1% tin - 0.4% silver. Commercial copper operations avoid silver alloyed anodes because they are so expensive - again, having 20,000 large silver-containing sheets in working inventory makes for an ugly cash flow situation for them, although the zinc refiners all do it...Anyway, for a home user with only 1 small anode, that little bit of silver won't break the bank.
For "cheap conductive coating" - you are out of luck. Electroplaters typically use either a copper powder dispersed in latex, or silver powder dispersed in latex. These coatings last long enough to plate whatever decorative coating is going on top, but this will never survive long immersion (like in a cell). They are very, very expensive (think 100's of dollars for a few ounces). Graphite or better, graphene dispersed in epoxy can also work, and is a little more durable, but difficult to get right. It might require sanding to expose sufficient conductive carbon. It is also expensive.
Paraffin dusted with lamp black (graphite) isn't even slightly durable, nor does it last more than a few minutes when immersed. It is meant to provide a conductive surface for a quick coating of copper, which is then bronzed. You can literally peel the coating on baby shoes off with your fingernail if you find one of the seams.
Best Regards, Gerald