a number is smaller than a string and faster to compare against but other than that it doesn't really matter.

If I understand you correctly, the main thing is to try pick an "unlikely" number. This way there is less chance that a random packet that happens to be using the same port as you will be misidentified as a legitimate attempt to talk your application's custom protocol. Use a random number generator - choosing the number yourself will almost certainly bias the results towards numbers that humans find "interesting" or "random". Do a search to see if the number you generate is already used - colliding with a existing protocol is exactly what you are seeking to avoid!

You can get away with including such identifiers with "anonymous" packets, such as connection attempts, broadcast discovery or server metadata queries. Once the client has successfully connected, the value of including such an identifier is much lower.

To be clear, it does not and cannot give you any real confidence as to the origin of the packets - you would need cryptography for that.

Thanks for answer!
I had to convert the protocol ID from haxedecimal int into char string anyway so I was sending somehow string at all. Therefore I guess I'll make up some protocol ID consisting of 4 chars ^^

It's generally called a FourCC 'magic number'.

It's a poor way to secure your communications, but there you go.

Protocol ID has nothing to do with "security" or "trust." It has to do with telling apples from oranges.
There are a few cases where you want to easily be able to tell your specific protocol packets from other UDP packets on the wire:

1) Someone might be sending UDP port-mapper packets, or other UDP packets, to your server. There might even be some other service that picks the same UDP port number, running on the same network. You wouldn't want the server software to process a packet you explicitly know is NOT formatted according to your protocol. Thus, these header bytes allow you to cheaply discard obviously unneeded packets.

2) You might want to sniff packets on a network, and quickly be able to tell your protocol packets apart from other packets that may also go on the network. This lets you apply a simple filter in Wireshark etc and easily make sure you're only looking at "important" packets. You could even take it a step further, and write a protocol detector/analyzer plug-in that would decode the packets for you when it saw those header bytes.

3) You might want to update the protocol version later, and prevent incompatible versions of the game from speaking to each other (to avoid crashes and almost-work problems.) Just bump your protocol magic number by 1 when you make an incompatible change, and you get that level of versioning for "free."