I know you said don't ask, but with the freezing mishap what type of worm was it?
My filtration is a little hard to describe, it was designed by a friend who customized the tank for me. In one back corner inside the tank, there's a chamber that houses a normal aquarium pump with a filter on the intake. It lets out into a u-shaped chamber in the other back corner where the filter foam is, so the water is forced up through the foam and then comes out at a v-shaped cut in the plastic housing. It doesn't splash or anything so I doubt it does much aerating. I also have a flow control valve on the pump output and keep it pretty low.
I am looking at getting him a 30-40 gallon tank soon (assuming we make it through whatever's going on with him right now), so filter recommendations would be great!
In answer to your question, I believe they were canadian nightcrawlers--which is incidentally the worm type that I have found works best for my axolotl and the kind I would recommend. Again, this was an unrelated incident from many years ago. Long story short, they exploded. It was gross. Anyways, I know you don't want to deal with live food, but the additional movement may help to stimulate your axolotl's desire for food. Other good options include European nightcrawlers or red wigglers. Some axolotls don't like certain kinds of worms, but there are things you can do to fix that. If I remember correctly, some people might even boil their worms? I would double-check that, but it could be an option for you.
Here are the links to the products that I use on my 20 gallon (let me know if they don't work, I can update them if necessary):
Filter:
Amazon.com : AQUANEAT 4 Pack Double Bio Sponge Filter, for Fry, Betta, Shrimp, Nano, Aquarium Fish Tank (Large up to 55 Gal) : Pet Supplies
www.amazon.com
Air pump:
Amazon.com: Tetra Whisper Air Pump 20 To 40 Gallons, For aquariums, Powerful Airflow, Non-UL Listed : Everything Else
www.amazon.com
The only other thing you need for this set-up is standard airline tubing. If you're looking for other info/problem-solving issues, I'll add some down below. Sorry in advance for the short novel.
In terms of set up, it's really pretty simple. The filter suctions to the inside wall of the tank. You attach the tubing to the thinner clear tube. The other end of the line attaches to the air pump. The air pump is plugged into the wall.
You will want to make sure to place the air pump somewhere above the aquarium's water line. This is to prevent electrical shortages in the pump. Basically, if the pump shuts off for any reason, you don't want water flowing "backwards" through the tubing into the air pump due to gravity. Ideally, you will have a shelf or some other platform. I personally use one of those insertable locker shelves, which I placed next to my aquarium and which ends up being just taller than my 20 long.
You may notice that, despite having only a 20-gallon, I use a filter/pump combo that are rated for up to 55 gallons and 20-40 respectively. I usually like to go at least a size up because, as I have no doubt you know, axolotls produce a lot of waste. At the same time, these sponge filters don't produce a lot of flow.
If you are concerned about too much flow, however, you can aim the output at the wall of the aquarium or use a valve on the tubing. If the flow seems decreased or there is not enough, you can always add another. This is hard to describe exactly, but one possible cause for a sudden decrease in flow could be that the air input tube becomes misaligned. It's pretty easy to fix, you just have to twist it until it's in the right spot.
One of my favorite things about this filter (other than it's great efficiency and low flow--oops, I'm sounding like an ad, lol) is that it has two sponges. This makes it really easy to replace one at a time without crashing your cycle. I'd recommend that each sponge get replaced every 3 months or so, but more often if you have a lot of build-up. For regular cleaning, I usually just squeeze out the debris in the old tank water when I do my weekly water changes. There are some replacement sponges on Amazon; just make sure you get the right size.
I personally like to replace the filter itself every 6-8 months or so, which is easy since they're pretty cheap. I do recommend always having a back-up if something ever goes wrong (to be fair, I have this policy with just about everything axolotl-related, lol). You can also easily take apart the filter into 8 pieces (excluding the sponges, so technically 10) for transport or for cleaning.
Okay, now a couple of things about the air pump. It actually is really REALLY quiet, but sometimes things come loose in production or transport. I recommend plugging this in before setting it up, just to check if it's working properly. If it's not, it will be VERY loud. The issue is fixable (took me about 20 minutes and a YouTube video), but if you'd rather not go unscrewing things, it's pretty easy to just exchange it for a working one.
Like I said, this thing is super quiet, but it does vibrate quite a bit. It has rubber feet to absorb the vibration, but if you want to decrease the sound even more, you can just slide a soft-cover book or a computer mouse-pad underneath. Just make sure you don't use something that can block the input, which is on the bottom of the pump.
Okay, sorry again for the novel. Hope if helps you/anyone else looking for info. Let me know if you have any questions!