Smartphones are one of the most used possessions for people fortunate enough to own one. So you should make sure that the phone you plan on buying is one that will keep you happy for a long time, especially since most people stick with one phone for 2-4 years before upgrading.
Some of the main criteria you should judge phones on are:
Screen (Size, resolution)
Since this is what you'll be looking at most of the time, it's one of the most important features of a phone. Larger screens make watching videos and reading text much more enjoyable, but they're also harder to use with one hand (especially for people with small hands) and may not fit in your pocket. If you have average sized hands, I'd recommend a screen size of around 5 inches. The higher the resolution, the crisper and nicer everything will look, from videos to simple text. I recommend not settling for less than 1080p, but if you're on a tight budget, 720p is still not bad.
A camera is made up of many individual components, so instead of trying to understand all of them, I recommend checking a phone's camera's DxOMark score. DxOMark rates all aspects of the camera individually, and gives it an overall score. Keep in mind that more megapixels does not always equal a better picture, and that a good single lens, like the Pixel 2, is better than two bad lenses.
While you can buy phones based off of reviews or the above criteria, at the end of the day, you have to decide what's important for you
Batteries are measured in milliamp hours (mAh in short), and generally, the higher the mAh of a phone, the longer the phone will last on a single charge. If you plan on buying an Android phone, I recommend buying one with at least a 3000mAh battery
Processor and RAM
Both of these things are what power phones, and explaining them in detail, would take a long time, so just keep in mind that 4GB of RAM, and Snapdragon 820 or above (The higher the number, the better) is ideal for Android phones. If a phone uses a different processor, that isn’t Snapdragon, you can search what its Snapdragon equivalent is. Unless you plan on gaming, 4GB of RAM and a Snapdragon 820 should be enough.
The four criteria mentioned above are the most important for judging how good a phone is, but there are many more, smaller factors, such as:
The majority of phones have at least 32GB of internal storage, which is enough for most people, and a micro SD card can be used to add more storage to any Android phone which supports it.
Some phones support wireless charging, which is self-explanatory, and many phones can be charged very quickly using quick charge (Or another form of it).
Almost all phones have an IP rating which tell us how water and dust resistant a phone is. Unless you're the type of person who drops their phone in the bathtub, an IP rating of 67 will be enough to keep it safe from dust and splashes.
Some people just prefer iOS (OS of iPhones) over Android and vice versa, so if you feel more comfortable on one system, I'd recommend buying a phone that uses that OS.
While you can buy phones based off of reviews or the above criteria, at the end of the day, you have to decide what's important for you. Unless your budget is well above 700$, you're also going to have to decide what compromises you are fine with, be it camera, battery life or anything else. For example, having a good camera is a necessity for people with thousands of followers on Instagram, but it's completely irrelevant for people who don't take pictures at all.