It is recommended to print with 4 perimeters/outer walls and a 20% cubic infill. This is what has been tested and it works well and the print times are reasonable. 0.15mm layer heights give a great result but 0.20mm will also give acceptable results and faster print time.
You will need at least 180x180mm print bed and at least 110mm of Z travel. You could further cut the poles to reduce the Z height needed if required at the expense of potentially seeing more seams. You could hide this with some creativity by alternating colours to hide the seams and use them as a feature.
On the Prusa i3 MK2S using the 0.20mm 100mms Linear Advance profile, with 4 perimeters and 20% cubic infill there is around 36 hours of printing required to complete the basket. No supports are needed, the cage has some overhangs but they have been carefully modeled to minimise problems.
When printing the poles ensure you have good bed adhesion and consider adding a brim since the contact area on the print bed is relatively small and the parts are very tall. Also note that when slicing the Basket_cage.stl part you may experience lengthy slicing times as the model is quite complex.
After printing drill out the pole sections with a 10mm drill bit. It will do very little but it is necessary to ensure the poles will slide cleanly over the threaded rod and that there is actually 10mm of clearance.
The other parts are good to go straight off the bed. If you added a brim to the poles make sure to clean up the area it was removed from. The cage and top section can see some stringing so if you have a hot air gun you can remove the fuzz with a quick pass over them (do not linger, particularly if printed with PLA).
Visually inspect all of the printed parts and make sure all of the holes are well formed and test fit the pole sections to the stand, cage and top to ensure a good fit before preparing for assembly.
Prepare the threaded rod by cutting it to length (445mm). If you did go with stainless steel then an angle grinder will save you a lot of time over a hacksaw. Before cutting put your M10 nut on the rod so you can unscrew it over the end to clean up the threads on the cut area. Take care, the rod will be very hot after cutting, let it cool down before inserting it into the printed pieces.
For the chains you will need to take the lengths of chain and break them up into segments. You need 12 segments of 15 links for the outer row and 12 segments of 12 links for the inner row. Carefully count out the links and hold the last one. The link will have a join, align your bolt cutters to the join and cut the link. In the chain used in the bill of materials the join is on the short side of the link.
After the link is cut take your two needle nose pliers and grip each long side of the link and gently force the cut open. It only needs to be enough to slide the next link off and back onto the 38mm solid center ring. The link counts include the broken link. Repeat until you have the needed number of segments.
With all of the segments prepared take the 38mm solid center ring and feed each segment on at the broken link. After putting each link on the ring take your pliers and close the broken link to fix it to the ring. Do not apply excessive force when closing the link as you can easily crush the link. Each ring should have 12 segments of chains of the same length.
Now take your 24 key rings and loop them onto the other end of the chain segments. Once they are all looped on you are ready to attach them to the basket. The key rings loop onto the holes in the Basket_top.stl part. When looping them on you may find it easier if you force open the key rings with a small screw driver to get them over the printed holes.
Loop on the inner chains first. Make sure that they are put on in the same order they are arranged on the solid ring. Failing to do so will prevent the chains from hanging straight. You should also try to ensure when looping the key rings on that the chains are not twisted.
It helps to pick up the solid ring several times during the process to ensure everything is falling correctly. After the inner row loop on the outer row. When finished turn the top right way up and check the chains hang correctly and the solid rings are relatively flat. If you have to untwist any chains it is now easier to unloop the chain and leave the key ring on the plastic part when adjusting.
The most tedious part is now over and you can finally assemble the actual basket. Take your threaded rod place the M10 washer on one end then the M10 half nut. It should be all the way at one end. Now slide the stand over the rod then the bottom most pole piece which slides into the stand. Slide the next pole piece on (the bottom section is the two shorter poles) then the cage, then the next two pole pieces, finally the top with the chains, making sure to slide the solid rings over the center pole.
To top off your basket place the joiner piece on top, then put the remaining M10 nut into the slot on the top plate piece. Screw the top plate onto the threaded rod. As it gets closer to the joiner piece line it up with the faces of the top plate and screw them on together. Screw it only finger tight initially.
Now take a 17mm spanner and hold the nut on the bottom of the basket and gently tighten the top plate with your hand. As you tighten the basket all of the pieces will push together to stop them moving around. Do not over-tighten or you risk breaking things.
When everything feels solid and the chains are hanging correctly screw in the feet to the stand and adjust to keep the bottom nut clear of the ground and to level out the basket. Stick it in the pool room and enjoy!