This is somewhat variable depending on the company and also depending on the size of the budget unit. Decisions in a company are often made by the budget unit (usually a department sometimes a division), although computer equipment may be sourced by IT.
In all honesty, if you are a regular individual contributor - don't overthink it. If there is something that would honestly help you do your job better and/or with less risk of long term damage to your body - it's better to ask than to try to figure out whether you will get a yes. You won't have all the answers. Just make sure you really can be more productive and/or helped by the equipment. There's a lot of gimmicks out there, and figure you can't ask for everything - so start with the high priority stuff.
From the Manager Perspective
Here's the questions that the approver may have to answer:
Would it be crazy to buy one for everyone? The sanity check is both the multipler (we have 100 people, this costs and extra $100, so we are spending $10,000 - wait! that's a drop in the bucket compared to the sum of everyone's salaries!). But it's also other conditions - for example - 2 monitors in a lab with limited desk space, or 2 monitors in a building with horrible electric (you will keep flipping the circuit breaker). A smart manager only has to live through a snafu like this once before they start considering this picture.
Are you different? For example, if you are the GUI guy, getting you a better monitor makes sense, and doesn't mean that they have to buy everyone one.
Is there a supplier relationship? Often a big company buys from a single producer - so you can have any HP machine, or Dell monitor, but you can't have anything from Toshiba.
How limited is IT? If this will cause endless woe with the IT department, it's not worth it.
Is this is a medical condition? Medical conditions trump a lot of things, and also give the manager a bigger point of power if demanding a change in rules.
What does the budget look like this year? Sometimes at the end of the year, or the beginning of the year is the best time for making requests. End of the fiscal year is great if there is slack in the budget, then the boss wants to burn through it (you may even hear the "let me know if you need anything" request about this time). Beginning is great if you typically run at or over budget, since the new budget may mean a new supply order at the start of the year.
How old is your current equipment? Often you can get a change in equipment when yours is end of life, but it's a major pain to exchange during the equipment's lifetime.
Can there be a switch - the end of life limits are less important if you can find a trade in the company (I did this when I realized my laptop was too heavy and too powerful - I had a developer who wanted the power, and didn't need to transport it - we switched).
Knowing some of these may help you negotiate the getting what you want process... but don't overthink it. Just know the price, know the power of what you want, and be ready to articulate it. If the boss seems unwilling, ask why.
I appreciate that X is provided for me, but to help me be more productive I'd like Y because Z. Would you be willing to help with the cost?