Don't buy bitcoins using Coinbase without knowing what Coinbase really is (they have been accused of spying on users' money transfers...).
You can purchase bitcoins in many different ways :
If you have cash, you can check if there is any bitcoin seller available near you on localbitcoins.com.
You can also buy bitcoins using Paypal on VirWox, but be careful, this method takes you very high fees compared to others methods. You have to buy SLL coins with your PayPal account and then trade them for bitcoins. You can read a complete tutorial here: https://www.deepdotweb.com/buy-bitcoins-with-paypal-credit-cards/
I'm not going to list all the ways you can purchase bitcoins. There are too many. Therefore, I highly recommend you to read this wiki page that lists all the ways you can buy your first bitcoins: https://en.bitcoin.it/wiki/Buying_Bitcoins_(the_newbie_version)
Is that possible to book a slot place ? I mean, if I start to wear [banned mixer] signature today and that one of the slot becomes free tomorrow, will I automatically take the slot ?
As it was advised above, I would recommend using cold storage.
Another alternative could be Ledger hardware wallets, that's a good choice if you have the opportunity to invest money in securing your coins. It has a function that allows you to recover your coins if you lost your hardware wallets by using a recovery card QR code.