If I have a ten year old Honda Civic with 40,000 miles, is it considered a
 

'newish' car, or just old? I am wondering if I should store a car, or will it deteriorate?

maintain it drive it once in a while start it once a week and it will be fine

Its not considered new but it would be considered to be in "mint" condition. Meaning it looks as if it were new at the time it was released. Low miles and a nice exterior will put it in this condition. Hondas will last you forever though as long as you keep up with oil changes and things like that. I've got a 93 honda civic with almost 300,000 miles on the original motor and it runs great and it is in perfect condition on the outside and inside.

An old low mileage car. You can store it but it needs to be started and driven occasionally.

40,000 miles is nothing. I would say keep it in storage until you need it.

Its considered an old car, but unless theres any damage, due to the low mileage, its probably still a relatively valuable car.