I'd get a specialist equine dentist to come out and do his teeth for you. Vets aren't trained specifically in teeth so will just do a basic file of the teeth. A dentist has studied the ins and outs of teeth as a speciality so will do a more efficient job. It's like going to a doctor for a filling. They can have a go as they know a bit about teeth and mouths, but they're not going to do the greatest job!
Get the dentist out soon. Then at least you know how the teeth are looking. If they need to be done, then you know where to start from. And if they don't need to be done, the the dentist will tell you how long until they will come back to do them. Probably another 6 months or so. I prefer to get everything out of the way and start a fresh when getting a new horse.
I will get the farrier out, worming, vaccinations, and teeth done all within the first couple of weeks. Gives me a peace of mind.