Welcome to the forum from a Coupe owner.
When you say nothing in terms of history do you mean not even a service book? If it was ever serviced at a BMW dealer and you can find out which one(s) a quick phone call should allow you to find out what was done and when.
But I wouldn't be put off by that mileage at the right price - I had an E91 325i with the same engine that had done 139K and it ran really well.
It's worth checking the MOT History as that may give you a few pointers for things to look at.
Any Z4 of that age is likely to have corroded rear brake pipes - there is a cover where they pass under the floor roughly under the passenger seat, and the end of the cover tends to trap road debris which holds moisture.
They have an electric water pump and OEM replacements cost over £200 for the part (Pierburg is the brand you want) so it's worth asking if it has been replaced. If not, budget for one just in case. My 1st Coupe needed one at 60K miles, and my E91 needed one at 135K - probably it's second!
And it's worth checking the tailgate for corrosion. When it is open check around the edges.
Otherwise it's pretty much the same things you would check on any other car of that age and mileage.
But you can't see what the oil looks like by pulling the dipstick because BMW decided not to fit one.
You check the oil level by pressing a button on the dash.
Good luck, and don't forget we like to see photos.
