Sheep, I just ordered a new liner for my BPIaB (i already had the pool from previous HBs). They do an automatic next business day delivery. The midwives will come out to you from 37 weeks, but not beforehand. If you have time to practice inflating it and making sure you've got all the right connections, etc, for the taps, as soon as you get it, then i'd recommend ordering it at 36 weeks. It will be there the following business day, and you'll have a week to practice before it will have the chance of being used. If something goes awry (eg this bump decided to be footling breech until recent intervention), you may reconsider with different risk factors. It will save you a lot of faffing if you go into labour early, too, and don't get to use it!
Something else to investigate is whether your home birth team loan out pools.... mine do (though you still have to buy a liner and a hose etc to fill it). Your HB midwife will let you know.
If you're thinking of saving some money by buying the pool 2nd hand, you might want to get it earlier just in case there is a delay or some issue with the pool. Mind you, if you're thinking of getting one 2nd hand, you could PM me; this will be my last, and i've got all the kit :-) (you'll still need to buy new hose and a new liner, though!).
WRT other things like breech, etc .... babies can be breech right up until the end, and turn in labour! You can still have a breech baby at home, but consider how they are positioned - eg footling breech (feet first) has 18% chance of prolapsed cord (though feet at head is 'fine'). I was footling breech until i had an ecv to turn her last week (37 weeks), which worked (although usually on about 50% chance of it working); i wouldn't personally have taken the risk of a home birth if she hadn't turned, though i have a few other risk factors as well. If you've made it through to 36 weeks, you have no issues, baby is head down, then buy the pool :-) You can buy it as early as you like, but bear in mind that babies do what babies want to do and it may not go as you would like to plan for....
Best of luck with your HB!