many of the questions you ask are personal experiences.
there is no exact science in keeping axies.. only a few minor guidelines.
tankwise. if your axolotl can swim around, its big enough.
if you have an even bigger tank.. good for them. more cleaning for you.
i use a cannister filter, that came with the tank. and it works just fine.
my water is clear as crystal.
( which does not mean the water is clean, but i have testers for that )
basically, if the filter has the capacity to function for your volume of water, its all good!
that is why i chose not to change mine.. i am 100% sure that it will do, as it came with the tank itself.
as for your bottom, again.. you are free to do as you please. as long as you keep in mind that same things are bad for your axies, and your water quality.
it comes down to what you want, and how much cleaning you are prepared to do.
i decorated my tank with slabs of lime stone, and filled the "gaps" with moss balls.
some fern and other live plants are jammed between the slabs to make the tank look more allive.
i also added a styrofoam background in the color of my hides and rocks..
so it looks more like a terranium then an aquarium.
cleaning that is a terrible job, because they seem to aim for the hardest to reach spots, and poo there.. but i dont mind.
i can spend hours on end looking and making sure everything is clean and good for the axies.
if you want it nice and easy.. leave the bottom bare, add an old flower pot as hide, make sure your filter outlet does not create to much disturbance in the water, keep an eye on the temperature and water-readings. and you are all good.
good luck on whatever you do, and dont forget to show pictures! also, if you cant figure it all out. search for help here. you can also pm me if you want.