I got pretty unsatisfied by the notation of amino acids in the literature. So I decided to make a cheat sheet for myself. I hope it helps you too.

The main idea is to develop intuition about solubility of the amino acids in water. The same intuition should be applicable to polar solvents in general.
For simple molecules, their solubility largely depends on polarity. For physicists, we are talking about the dipole moment of the molecule. The more polar the molecule is, the more soluble it is in water. Water molecules may surround the molecule and form hydrogen bonds with it. This enthalpic gain is higher than the entropic loss of the water molecules. That is why polar molecules are soluble in water.
By the same logic, carboxylic acids are more soluble in water than their conjugate amides. This whole idea of making a table about amino acids for myself started with my confusion about glutamic acid and glutamine. Counterintuitively, glutamine is more soluble in water than glutamic acid. The same goes for aspartic acid and asparagine.
The resolution of this confusion starts with recognizing amino acids as zwitterions. At pH=7, the carboxylic acid group is deprotonated and the amine group is protonated. The enthalpic gain of water molecules surrounding the zwitterion is now complicated because of the extra dipole-dipole interactions at three locations, promoting aggreation with other carboxylic amino acids. The same logic goes for the basic amino acids (histidine, lysine, and arginine).
The solubility of amino acids in water turns out to be pretty complicated. One might thing that the dipole moment of the side groups of the amino acids is the main indicator of the solubility of the amino acids in water but it turns out to be quite poor. The size of the side chain plays a large role in the solubility of the amino acid since the amino acids exist in a zwitterionic form at pH=7. The smaller the side chain, the more soluble the amino acid is in water. As a matter of fact, serine and amino are the most soluble amino acids in water. Alanine comes the third as the side chain is a methyl group.
It is noteworthy that the fourth most soluble amino acid is proline which is often considered as a hydrophobic amino acid- unusually high solubility for the side chain of the amino acid. Apparently, the pyrrolidine ring of proline can weakly interact with the ring of the other proline molecules, allowing them to form oligomers. These oligomers can be solvated by water molecules, making proline more soluble than expected. I’d like to find firm evidence for this claim, but I couldn’t find any. I came across a paper whose abstract suggests this mechanism.

For anyone interested in the topic, you are more than welcome to download a cheat sheet I made for myself.
What is nice about it is that you can sort the amino acids by their solubility in water, dipole moment, and the size of the side chain, etc. Amino acid cheat sheet: Amino Acid Cheat Sheet (Excel)