Before we dive in, there is a lot of subjectivity involved such that you may prefer what I see as low quality meme avatars over what I think high quality are. One avatar can prob fit into multiple categories and some may even contradicting with other examples (likely the typical good quality avatars and Generic/Misc/Self interest avatars). The descriptions explaining my reasoning are likely very flawed and I can't be bothered to make sense at 3am.
High Quality Avatars:
This is the self drawn/made category. The person who has the avatar drawing shows that they are devoting their time, creativity, and care to make something that stands out and unique to them. They will almost certainly never change their avatars.
Logo type avatars. Identifies the person's style and is unique to them. These rarely change if at all
These are just eye catching, making it easy to identify a person to. Either something sticks out or something isn't right, but it got your attention and you get who it belongs to burned into your memory.
These are the typical good quality avatars that are subject to change every now and then. They are high quality (not pixelated or smudged like mine), and pleasant to look at.
Medium Quality Avatars
Avatars with beautiful artwork, maybe a bit complex, that doesn't really relate much to the identity of the person
Cool looking avatars that have maybe too much going on
Generic/Misc/Self interest avatars. Convey what the person is currently liking and is subject to change. Often the image is not the best, but they do serve their purpose.
Selfies/Photos. Whether they have your identity or not, it's not as good to look at most of the time unless you make art of it.
Collab fever avatars. Some decent effort goes into those, but they are just a fad and don't do justice in connecting to the person's identity.
Low Quality Avatars
These likely means more to the person who's avatar it is than to other people. They are not memorable, however.
1 sorry for one example, these are hard to find.
Meme avatars that can probably be found online somewhere. If not, it likely took enough effort to qualify as a high effort shitpost.
I have no idea why...