Hi Enyer! This will depend on context. All three forms can work in multiple settings, but which one you choose is strongly determined by 1. what you want to convey and 2. your relationship with the receiver of the message.
In terms of formal settings (e.g. professional workplaces), I would recommend choosing 2 or 3 (2 might be my personal preference). For instance, a sentence such as "Please send me a message once you've received the form" would work well and flows better than a version with 3. If you have a more personal relationship with the receiver, you could also say "Please message me once you've received the form" but it's not wrong to use one versus the other.
Grammar note: 2 and 3 are essentially the same sentence, just with a change in the placement of the indirect object (me).
Hope this helps!
-Michelle