+1 on what Foxes said, there, especially the part about watching him get all groomed and tacked. Even better if you can watch him be caught in the paddock first.
Good on you for considering an older horse. A lot of people won't, but they're missing out on the value that an experienced horse will bring to the picture. FWIW, these days, they're not considering horses as being "senior" until they're well into their twenties so your guy is still middle-aged. Prime of life!
Be sure to get the PPE. Get bloodwork done, too, even though it means an extra charge. Since this isn't a horse your daughter has been riding regularly, you do want to get the vet to check for Substances that might have been used to calm down a frisky horse (and believe me, my 18 yo horse is proof that you're never too old to act like a blazing idiot). Also it's a good idea to get the bloodwork because it can show potential issues, like metabolic problems, etc. before they start to create symptoms...and even if the bloodwork is totally clean, then you have baselines for later in case the horse gets sick. The extra $150 or whatever they charge for this part of the PPE is well worth it.
I would also ask around to find a vet who does a really good PPE. Most of them will do them, but some vets are more thorough than others. You want the thorough kind. Be sure that the vet is doing a joint exam, flexion testing, etc. and that the vet knows what you plan to be doing with the horse (and be totally realistic with yourselves when you come up with that answer). The PPE takes place in a context, the horse doesn't get a "pass/fail" but the vet will let you know if there are issues that s/he sees, or potential problems, and should also comment on the horse's suitability for the intended use (which s/he will need to get from you). If you're planning on jumping with this horse, be sure that the vet knows that.
Also, my best advice is to get a really good guide to all things horse - there are lots of these, and you can find them on Amazon. Find one that's been written for first-time owners that offers a pretty comprehensive overview of nutrition, fitness, exercise, grooming, health, etc. Look at the "health" section just enough to make sure it's the thickest part of the book, and then put it down and use it for a reference. Otherwise, it's far too frightening. :)
Then line up a round of Paxil for yourself, because there is absolutely nothing to breed anxiety, sleepless nights, and panic like horse ownership. It's almost worse than having kids. At least the kids are sleeping right in the other room where you can go check on them to make sure they're still breathing. The horse usually lives in a barn down the road, and it can be difficult to explain how come you're there at 2am because you had a dream that the horse got sick or injured.
That last paragraph is *mostly* not serious. And I will say that - sleepless nights and all - owning a horse has been an amazing and incredibly rewarding experience.