Melden has a far wider scope (beyond advance registration), so in everyday language I'd usually use anmelden for that unless strong precedence in a given context suggests otherwise.
Anmelden has connotations of a formal procedure, of a list being kept somewhere, and of an effect of that registration in the future. Compared to this, the focus of melden is more on communication: conveying relevant information to someone in charge. This applies to the general meanings, like that of raising your hand (to convey that you want to speak) and of reporting an incident after the fact (to convey whatever you know about it).
einen Sportler für einen Wettkampf melden
In this case both alternatives would have been possible. I'll try to put the slight nuances in connotations into words. Reading that example as written I've got a mental image of the trainer walking over to the organizers and letting them know that the athlete in question will be participating. If you had used anmelden instead it would be the trainer writing the name of the athlete onto some whiteboard so that he will be allowed to participate. The former was “he will participate, therefore I should register him”, with the registration as a consequence, while the latter was “I need to register him so that he can participate”, with the registration as a prerequisite. In the former the organizers as recipient of the information are important, in the latter case the whiteboard as a registry is central. Personally I'd have used “anmelden” here.
As I said I'd usually prefer anmelden since the other meanings of melden could lead to possible misinterpretations. I'll give some examples.
Ich möchte Maximilian hier in der Schule anmelden.
would be a parent signing up their child for first grade next year, while
Ich möchte Maximilian hier (in) der Schule melden.
might also be a neighbor of the school handing in a complaint about a problematic child. Melden used for someone other than yourself can easily obtain negative connotations. In these case it's often more about reporting some issue or telling on someone than about registration.
Ich möchte eine größere Überweisung anmelden.
would be a customer informing their bank about a planned large transaction, making sure it will get cleared without causing any issues. On the other hand
Ich möchte eine größere Überweisung melden.
might be an investigator telling their superior about a past transaction of suspicious volume. So here the temporal aspect is again very pronounced.
Ich möchte mich für die Konferenz anmelden.
would be a registration of a participant of some conference while
Ich möchte mich für die Konferenz melden.
could be a student volunteering to help organize the conference without actually participating. (Freiwillig) melden as translation for volunteering shouldn't be confused with the meaning for advance registration, even though volunteers often get registered at some point.
Ich habe mich beim Arzt angemeldet.
means I've made an appointment with my physician, while
Ich habe mich beim Arzt gemeldet.
means I actually had some conversation with him, with melden indicating communication (usually informal), not registration.
Another thing worth noting is that melden in the sense of reporting can be followed by a dative, indicating the recipient of the information. For anmelden you'd use a preposition. So you could have
Ich muss mein Auto der Gemeinde melden.
Ich muss mein Auto bei der Gemeinde anmelden.