You will need a tub with a lid otherwise the bottles will bob around in the surface if the water and the won’t all be submerged.
I just took 2 Tupperware style Ikea box from my kitchen. They sat inside each other in the suitcase and filled them with clothes so they did not really take up any room.
If your airport has a boots you can preorder formula and nappies to collect airside. I popped the nappies into the buggy bag along with buggy before it went into the hold so we did not have carry it on the plane.
Milton do a travel steriliser that fits 1 bottle in. In theory any clean plastic container with a lid will do, but the travel sterilisers have the lines on so you put the correct amount of water in (as do the normal Milton sterilisers). I prefer the Milton fluid over the tablets as I found the tablets never fully dissolved. But either will work.