I am going to buy a new clarinet, those choices I am considering include Buffet R13, Buffet RC and a second hand Buffet Festival. Can anyone suggest what I have to check up in buying it?

See what fits your price range, try out half a dozen or so of each model (test the used festival you want to buy), and see what works best for you.

nEVER BUY AN INSTRUMENT UNLESS YOU Are sure it fits you.

I`m talking hands and length of arms.

Then price range comes into factor along with tone quality

Intonation; response.
Tone quality is YOUR responsibility, and is determined more by your mouthpiece/reed than the clarinet itself.
If you can afford the ones that you mentioned. money shouldn`t be a problem.

Well it`s true that tone comes from the player, but it IS a large factor if you`re testing clarinets. Why do you think R13s are so popular?

Again, ask for several clarinets from each brand - you probably also want to think outside buffet - and pick which individual clarinet suits you the best. Since money doesn`t seem to be the restriction, the best way to do would be not even to look at what model it is. Things you`re looking for:

Tone - Does the clarinet have the sound you`re looking for?

Intonation - Not neccesarily with a tuner. Check if the clarinet is in tune with itself. Check intervals and play some slow scales.

Response - Does the clarinet articulate cleanly? Can you play notes at the dynamic extremes?