@baileymvidler I recently have just gone through the process of submitting to agencies, and I am slowly picking up submissions to publishers.
I agree with @NessIllustration on following agencie's submission guidelines.
Postcard is not considered an agency submission in my understanding. But it is a way to get eye balls on your art. It never hurt to reach out with postcards to both agencies and publishers (but right now, people are working from home, I would hold on to postcard campaign for a while)
With agencies, one of the most important thing is to do your research. It is really important to find an agency that fits with your art, and you are comforatble with the way they operates. It is probably a very good idea to talk to some artists who are represented by the agencies you want to apply. I spent a lot of time put together a list of agenices I want to apply, and I read as much as I could about the agencies, looking through what books they have helped putting out, and I also look for podcasts that interviews agents from the agencies I want to apply. I am looking for agents that talk about art and business in a way I understand/agree/admire.
Most of the agencies will not reply, and so does publishers. That is the strange standard in the publishing world today, an unforturate and annoy truth for us illustrators. So the best way for us to deal with this is to expect no reply at all. And if someone send back a personaised reply, that means he/she is interested in yoru work, and you can put them on the list of "apply later".