"Dates" covers fruit so different in size, texture, sweetness and price that the word is nearly useless on its own. The two varieties most people are choosing between are Ajwa and Medjool, and they are not substitutes.
Ajwa
Small, dark — almost black — with a fine wrinkled skin and a soft, slightly dry flesh. The sweetness is mild and restrained, with a faint note that people variously describe as raisin-like or lightly savoury.
Ajwa come from Madinah in Saudi Arabia and carry considerable religious and cultural significance, which affects demand and therefore price independently of any culinary consideration.
They are a fruit you eat one or two of, deliberately. They do not dominate anything you put them in.
Medjool
Much larger, glossy, amber-brown, with thick flesh and a soft, almost fudgy texture. Far sweeter than Ajwa, with strong caramel and honey notes.
Medjool are the dates most people picture when a recipe says "date". They blend well, they carry a filling, and they are the obvious choice for anything where the date is doing structural or sweetening work.
Choosing between them
If you want fruit to eat as it is, in small quantity, with restrained sweetness: Ajwa.
If you want sweetness, bulk and texture — for stuffing, blending, baking, or as the sweetener in something else: Medjool.
If you are buying for a gift, Medjool photograph better and read as more generous because of the size; Ajwa read as more considered. That is a genuine difference in how the two land, not a quality judgement.
How to judge either one
Variety sets the character. Condition sets whether it is any good, and condition is what most people fail to check.
Look at the skin. A fresh date has a slightly translucent, plump skin. Deep, dry wrinkling across the whole fruit means moisture has gone.
Look for sugar crystals. Small white crystals on the surface or at the stem end are crystallised sugar, and they indicate a date that has been stored a long time or through temperature swings. Harmless, but it is an age marker.
Press gently. It should yield easily. A date that resists has dried out, and while soaking recovers some of the texture it does not recover the flavour.
Check the stem end. It should be intact and clean. Dates absorb odours and moisture through a damaged stem end, and that is usually where spoilage starts.
On size grading
Medjool are graded by size — commonly small, medium, large and jumbo — and the grade is largely about presentation. A jumbo Medjool is not a better-tasting fruit than a large one, it is a bigger one, and the price premium is mostly aesthetic.
If they are going into a blender, buying down a grade or two is the easiest saving available in this category. If they are going on a plate in front of people, size does real work.
Storing them
Sealed and cool. Dates are hygroscopic — they pull moisture from the air in a humid kitchen and lose it in a dry one, and neither does them good.
In a sealed container they keep for months at room temperature and considerably longer refrigerated, though cold firms them up. If they have gone firm, a few hours at room temperature usually brings them back before you resort to soaking.