Many people send a PM, and then also post that they have done so. I'm not sure exactly why, but maybe just make sure the person knows a message was sent.
The selling process is up to you and the buyer, and you should see what other people post as far as rules, like only taking PayPal, or using a service like Escrow.com.
The general process for less expensive domains is that if the seller has a good trader rating, the buyer sends the payment. Then the seller pushes the domain into the buyers account where the domain is registered. In your case, you have a zero trader rating, so a buyer may ask that you transfer the domain to them first before they will pay you. If THEY have a good trader rating, then this should be safe. If not, then you may want to use another member here or a service to provide some protection for both parties.
The more valuable your domain is the more careful you should be. It is very rare, but on at least one occasion a user with good trader rating had his account hacked, and someone sold a domain to a person they THOUGHT was the good trader only to find they pushed the domain into an account of a crook.