To start your classical guitar lessons, you need a classical (Spanish) guitar.
There are plenty of music stores where you can buy one. The sells man usually are pretty helpful, in general they do a good job, some of them are even able to strum some chords on the guitar, trying to impress the costumer. But as you are a beginner and you never had guitar lessons, it is easy to be miss leaded by them. In the and of the day their job is to sell. So its not a good idea to relay on their opinion 100 per cent, with all my respect.
The best option is to ask your potential Classical Guitar Teacher, before your first Guitar lesson.
Your guitar teacher in most of the cases, will provide you with information not only what kind of guitar you need, but also what size, what brand and where you can get it for the best prize.