Tricky. £1000 is well more than necessary for an old banger but not enough for a good new piano. You kind of need to be lucky and/or know what you're doing. Or be prepared to pay a specialist to take a look, which might be justified at the price point you're talking about.
I would say if there's one thing that's not negotiable in buying a piano, it's tuneability. As long as the piano can be tuned up to concert pitch and hold its tuning relatively well, then other factors can mostly either be fixed or won't cause too many problems for beginners. But a piano that is really beyond holding its tuning never will, and learning the piano on an out of tune instrument can be unpleasant and musically counterproductive.
It's for this reason that, although I don't really like them, I would often agree with the advice given above to buy a digital piano for that kind of money. In fact you shouldn't need that much and should be able to get a decent Yamaha or similar for 500ish. I would say if someone's willing to spend c. 3K upwards, definitely get a real piano as it's the best thing for learning on, and you can get a decent new one that will be reliable and tunable. However if you're spending in the hundreds rather than thousands, you're likely to get a better digital piano than acoustic one for that price. The more straightforward digital pianos also hold their price pretty well so if your daughters are keen, you could sell it in a few years for probably 2/3 of what you paid and then know it's worth investing properly in a good real piano.
I would personally advise against buying an old banger for a hundred or so off ebay. Unless you can see it and really know your stuff, it's likely to be permanently out of tune and frustrating to play. And then with another few hundred quid to move and tune it, you've wasted a substantial sum.
If you're anywhere near London you could try somewhere like this:
www.pianoauctions.co.uk/
I bought my grand at a piano auction that has since closed down for £600 and it's lovely. You can go along beforehand to try the pianos, and you could take someone who knows a bit more and pay them for their time, for advice about what to bid.
Failing that, 3K for a decent Steinway sounds reasonable. Again though I'd get it checked over. For that price it would be worth it.