I have a fair bit of experience with potted outdoor water plants. So I can tell you a few things, but largely from the perspective of what is good for the plant, not necessarily the aquarium.
Soil
The type of soil you want for most plants is ideally a light clay loam. You are trying to make a light rich pond mud sort of stuff. But basically anything with just a teeny bit of clay (but not too much, especially in an aquarium) is good.
Try handling the soil when it is just very slightly moist. If you squish it in your fist and it holds form, but can be relatively easily crumbled again after, it is probably good. If you only have very sandy soil while not great it isn't so bad. However if your soil is very solid heavy lumpy clay that's probably bad.
The soil should have little or no organic matter in it. You don't need it, and it just rots (in a bad way) or floats away. The less the better.
When harvesting soil from the garden the easiest way to avoid a lot of sticks, twigs, worms, and tiny fragments of rotting organic matter, etc... is to just get the soil from a bit deeper down.
Pots
You can use any kind of pot or container that is aquarium safe. Submerged plants don't care about drainage holes etc...You can even use bags, cups, buckets, whatever.
Some aquatic plants have deep roots, but most prefer to grow their roots out rather than down, so you don't need especially tall pots, but wider ones probably are better.
Gravel
Gravel is not at all necessary for the plant or to keep the soil in. It might even be just a little bad for the plant.
But it MIGHT be necessary to keep axolotls or fish OUT. So it needs to be big enough your animals cannot shift it. Try not to crush the plant too much.
Soaking Soil
From the plant's perspective you can pot it and sink it in the aquarium straight away and it won't care. For quarantine people this might however be not so great. And for water quality you are likely to release a fair amount of mud by doing so. It should settle, or get filtered out, but you probably don't want that in an aquarium anyway.
BUT. If you have the plant now and want to plant it AND you want to soak/quarantine the soil for month or whatever that someone already recommended, just plant the pot and drop it in a bucket of water. It can release the mud there, settle, soak, quarantine and even grow and get a bit established. Over time the mud (gravel or not) will not just settle but form a sort of biofilm that will hold it in. Then you can just move the potted plant to the aquarium later.
The number one bonus of potted plants after all is that they are highly mobile. Meaning you can do things like settle them in somewhere else and only move them when they are super ready, and even trade them out to a bucket or pond in the sun if they look a bit sick in the tank. Even repot them without having to drain and clean out large portions of your tank if you need to.
Fertilizer
People will tell you never to use fertilizer in a fish tank. I somewhat agree. But outdoors we use it all the time, putting it in the soil in the pot (usually we put it in the soil in the bottom with a bit of paper under it and put unfed soil at the top to seal it in a bit). But that WILL still leach. So I would'nt do it in a carefully balanced aquarium.
The thing is though that if you really DO end up running it for as long as a month in a bucket or something then you probably can give it a very small amount of very weak organic fertilizer (a tiny pinch of blood and bone, maybe about a single pellet of dynamic lifter) and expect that to have been generally leached out or consumed by the time the plant goes to your tank. Don't try messing with slow release fertilizer, do NOT use any untreated animal manures, don't use synthetic fertilizers and stay away from "water lily tablets" all of those will cause serious difficulties even before you consider their almost certainly negative impact on an aquarium.
In the end plant food of any form is probably more risk than benefit. Especially if the plant isn't spending at least several weeks growing before going in your tank. And even without added food in the short term the plant will pick up some food from just water and the new raw soil, in the long run it should feed itself once it's in the tank.
