I'm writing in partial response to aBrav's answer. Since that answer, I got an ultrasonic cleaner myself, and I started waxing my chains. I started with a couple of lightly used chains which had been ridden with an oil-based drip lube.
First, an ultrasonic cleaner is not necessary to clean your chain for waxing, especially not if you're starting with a new chain. The link from Adam Kerin that was provided did say (first page, emphasis mine):
Not necessary unless preparing race chains / re optimising race chains and going for every possible watt saving.
Very handy for if have broken in chain (ridden 50 to 100km to break in with factory grease). A chain with a good break in in clean conditions will be a faster chain than a chain straight out of the box cleaned and waxed. However, the break in will bring in contamination. Agitated container baths will not perfectly clean from all tiny fissures, nooks and crannies. If looking to prep a fully optimised race chain by doing a break in with factory grease, an ultrasonic is a must or the break in will be negated by contamination imported that you cannot perfectly clean out via agitated container baths.
If you use an ultrasonic cleaner as the sole cleaning device, you may be disappointed, as I was. I did this in ignorance when I got one, and it took take a number of cycles to get a dirty chain fully clean. Considering that it's recommended to degas the cleaning solution (run the ultrasonic cleaner on the degas cycle for 5-10 minutes before putting the chain in to remove any dissolved air in the solution), this time adds up - you are heating the cleaning solution, then degassing it, then running the cleaning cycle for 10-20 minutes. You then need to empty the solution and preferably wipe the tub clean. NB: If there is dirt in the chain, you can see it drifting out from inside the rollers the second you put the chain in the ultrasonic cleaner.
Users are better off using repeated baths of traditional solvent in a plastic bottle, and you can optionally add an ultrasonic cleaner bath with cleaning solution as a last step before you rinse in alcohol.
If you do the above, I currently think that if you want to add an ultrasonic cleaner, household-capacity cleaners of the power mentioned in aBrav's answer will suffice. My own cleaner has 70W ultrasonic cleaning power (NB: remember that this is separate from heating power, and some cleaners may report total power as ultrasonic transducer power + heating element power), so this could plausibly be sufficient for personal use if you pre-wash the chain as described. However, do note that Poertner recommended an ultrasonic cleaner with 180W cleaning power, which is 1.5-2.5 times the power range that Kerin recommended. I'm not certain if Poertner is using this cleaner for his entire cleaning cycle, or just as a finishing step. I have no practical experience with cleaners that powerful. They might suffice as a primary cleaner, or not.
Some side notes:
If you are starting with a new chain, Kerin has advised that you can soak the chain overnight if and only if your solvent doesn't cause hydrogen embrittlement; many Simple Green formulations will do this, and this weakens the metal and can cause fractures, but mineral spirits do not and neither do many aerospace degreasers. One example of such a degreaser is Chemical Guys, recommended by Josh Poertner of Silca (link above), another example is Simple Green's aerospace formula.
You can obviously use degreaser in your ultrasonic cleaner, or Kerin has stated that you can actually use dish soap and water. Poertner has recommended plain deionized water, or deionizer water with a dedicated ultrasonic additive added. One example he gave was Shooter's Choice (link above). In my experience, deionized water is relatively expensive. I tried purified water, and I believe the results were at least adequate. As a bonus, the water step probably removed some of the residual degreaser film, meaning that I could use less alcohol to finish the chain.
Chains may have some or many parts coated with PTFE or a similar low-friction polymer, or they might get some sort of hardening to decrease wear. Adam Kerin said that more powerful ultrasonic cleaners than the ones he recommended might damage these coatings. I am not sure if he determined this empirically or through experience. Also, the higher-performance commercial waxes have low-friction additives like molybdenum or tungsten disulfide that are supposed to load up on the metal's surface and reduce friction. I'm not sure how much or if those additives benefit from the presence of low-friction coatings or not. Indeed, Silca is selling chains that were polished to reduce surface roughness, and that process must surely destroy the low-friction coatings on the chains (albeit Silca then claims to impregnate the chains with dry tungsten disulfide, which would presumably counteract that).