Why the screenshot method fails
Screenshotting something you spotted is the most common method and the worst one. Six months later you have a picture in a camera roll of four thousand pictures, no link, no price, no size, and no idea which shop it came from.
The photo is for you; the URL is what makes it buyable. Save the link even when you also save the picture.
The property that actually decides whether you keep using it
Whatever you pick, the thing that determines whether the list still exists in November is how long it takes to add something from your phone while standing in a shop or half-watching Instagram.
Under ten seconds and it becomes a habit. Over a minute and you will stop within a month, whatever you intended. Test that before committing anything to a tool.
Separate the list per person, not per occasion
One list called "gifts" becomes unusable by about item fifteen, because the only question you ever ask it is "what could I get for this specific person", and a single list cannot answer that without you reading all of it.
A list per person answers it immediately, and ideas naturally arrive per person anyway — you see something and think of somebody.
Write down why, not just what
The single most useful thing to record is the reason you thought of it. "She mentioned her kettle died" is worth more in November than the product name is, because it tells you whether the idea is still good — kettles get replaced, and a note like that saves you buying a second one.
It also rescues ideas that were nearly right. A note saying "loved this but the colour was wrong" turns a dead entry into a usable lead six months later, where the link alone would just look like something you already rejected.
If other people can see the list
Decide up front whether they can tell what has already been claimed. Two relatives buying the same thing is the classic failure at Christmas, and it is a property of the tool rather than of the people.
The lighter version of this, which is enough for most families, is simply being able to comment on an individual item. You do not need a formal claiming system; you need somewhere for one person to say "I'm getting this" that the others will actually see.
Check it in October, not December
Ideas collected in March go stale. Prices move, things sell out, and people buy the thing themselves. Whatever you use, open the list once in autumn and delete what is gone — it takes ten minutes and it is the difference between a list you trust and one you scroll past.