There is no one best way to do this, and as to the OP, the idea that ultrasonic is going to show its stuff on a "dirty" record is, I think you’ll find, not necessarily true. In many cases with used records we have no idea what contaminants they have been exposed to; ultrasonic is one tool in your arsenal to deploy. I combine cleaning methods, pre-clean used records (some of which are rare and of high value) and use ultrasonic, but the latter is not the only solution-- it may be good for records that have been maintained in pristine condition by audiophiles, but even in those instances, I often wonder what "cleaning" methods were used that left residue.
There are best practices to this starting with what archives do, including the Library of Congress.
There is no one wonder chemical and dealing with ultrasonic, there are trade offs-- you want to lower surface tension of the water, perhaps have some detergent to bind the contaminants, but the other side of the equation is how that stuff is removed once it has done its job. That, to me, is where the rinse step plays a role.
I’m not a materials scientist or bio chemist but have spent a fair amount of time digging down into this stuff and can defer to those with more knowledge than me. Unfortunately, most of the science of making records, at least in the published papers of journals like the AES, stopped in the ’70s. Cleaning agents are regarded as proprietary by their makers and in some cases, the manufacturer of an ultrasonic machine may insist that you use their fluid lest you violate their warranty.
If you are DIY, you have more options and there are a lot of fluid concoctions that people have shared on the web. Often, it is based on trial and error, or someone’s suggestion that a particular chemical or combination of chemicals works for them.
There is science to this, and it requires a methodical approach. As mentioned, Neil Antin has done an extensive study on record cleaning, the chemistry and methods. He is in the process of revising that study to account for ultrasonic cleaning and I hope to publish it soon. It will be available at no charge, and Neil has been generous with his time in working with users to help them address issues of detergency, foaming, removal of surfactant and the like.
As to investing in an ultrasonic machine as a one time proposition, the transducers will eventually burn out; there are equipment failures (witness the early AD teething problems which I gather have been sorted with the PRO model).
If one is looking for a simple, drop a record in and push a button type approach, the current in vogue machine is the DeGritter, with which most users report positive experience. I think you’ll find if you spend time with the made for LP machines that they are a compromise; thus, the need to use conventional manual cleaning for used records, in combination with ultrasonic. There is no one size fits all solution to this in my estimation.