Thinking of Homebirth, just not sure of everything needed for a waterbirth
As a retired homebirth midwife in Australia I can help. There are lots of types of inflatable birth pools around. Mine was a La Bassine. I loaned mine out but some women prefered to buy their own. Because of the number of people using the pool, I required that they buy a liner as that stopped one person birthing in a pool that someone else had birthed in. Even with good cleaning people don't like that idea.
You set it up where you wish to birth. A lot set it up in the lounge as that is usually a large room. You need to make sure you can get hot water in, usually from the hot water tap in the laundry. If your hot water system runs out then it boiling big pots of water on the stove.
If you are in a cold time of year, make sure you have some layers of insulating stuff on the floor under the pool, I usually recommend newspaper. Otherwise it is hard to keep it warm enough.
If you have a good air pump they don't take much time to set up. Do a practice run by 36 weeks and see how long it takes you. If you are afraid that you will birth too quickly then keep it set up but not fully inflated, helps stop it holing when the kids whack it with a toy. Duct tape can fix problems like that.
Try to have enough space all around the pool to allow the midwife or your support people to be wherever you need them around the pool. If you have it on carpet then use a new cheap tarpaulin to cover the carpet. Lots and lots of towels. I usually suggest a dozen, it can get wet around the pool.
The difference between a birth pool and a children's wading pool is the depth, the rigid sides so you can lean, and the inflatable bottom so that your knees are not on the ground when you kneel in the water.
Lastly you need to be able to empty it. It is fairly easy to siphon the water, just make sure there is somewhere to siphon too. Out of the door into the garden bed is a common one. If you have to empty and can't siphon you can buy a cheap 12V bilge pump from a camping and fishing store and connect it to a 12V battery and then the hose.
Hope that helps.