I have a 120 cm (4 feet) tank and I like to have my filter spraybar on one end of the tank and the air stone on the other end so that the surface is lightly moving in every part of the tank -> very good oxygen levels. My wild type also loves to take bubble baths over the air stone.
The most important things to get right away:
-the tank (80cm x 35cm or more floor space for one or two axies)
-filter (right size for your tank)
-water testing kit (liquid master test kits are good as they have everything you have to test in one package, test strips are good too as long as you are careful to store and use them correctly)
-ammonia to cycle your tank
-buckets, vacuum/siphon and a turkey baster for cleaning and water changes
-dechlorinator if you need it (I've never had to use anything like that)
-some hides and plants for your axie plus fine sand if you want to use it
-a fan/chiller to keep your tank cool if needed
-worms if you want to start a worm farm, otherwise don't buy them yet as it'll be a while before you can get your axies. If you want to buy food right now, get pellets that are specially made for axies