Hardly anyone here has their own public ASN. In your case, you would use the ASN of your provider, Vultr.com. Vultr has extensive documentation on their site, on how to setup BGP advertisements, although you do have to dig through their support docs a bit to find it.
Vultr will assign you a private ASN, which is then used for all interaction with them, even if you use multiple Vultr data center sites. The Private ASN is of no value outside of Vultr, it simply allows their setup process for easily automated. It was amazing (to me anyway) how easy it was to get BGP advertisements working. Literally within a couple of hours, a prefix assigned to you can be setup and be fully operational. They also accept email’d LOA formerly from BrianK, and I assume now from ChrisS.
So, here are my questions : Is an ARIN ASN number mandatory in such a situation ? If not mandatory, would it be a good practice to have one ?
It is mandatory. But like IPv4 addresses, they are a limited resource, and you need to have connections to multiple backbone providers to even apply for one. IOW, you need to be in the business. Nearly all of us here will use the Public ASN of our provider.
If so, would RIPE deliver ASN numbers to people or companies that do not own any IPv4 range (I am not the owner of my 44 subnet, ARDC just grants me the right to announce it) ?
There is no need to involve RIPE (or ARIN), nor any requirement to even communicate with them. ARDC grants the authority to your SP (Vultr) to advertise a specific prefix on your behalf, through the ARDC license or LOA process.