@sachaha If you don't need a laptop, as in, you're comfortable either way, then a desktop is the better option. Its components will be more powerful at a given price point, and it's much more upgradable and (crucially) much more repairable as well. Gaming desktops are generally built with standard components that you can find separately, meaning that if anything breaks, you can replace only that. And adding or upgrading a component is straightforward. In contrast, laptops almost certainly can't be upgraded past RAM and storage, and repairing is more complicated, and sometimes not possible, as well.
All-in-one PCs like the HP you linked are built like laptops, with the same limitations on repairing or upgrading. So if the choice is between a gaming PC and an all-in-one, I personally think it's an easy decision.
As far as monitors go, almost all of them are compatible with almost all desktop PCs. DisplayPort and HDMI are standard connections on all modern monitors and graphics cards; all you need is the right cable, which will probably come with the monitor anyway.
If you do need a laptop for one reason or another, I should be able to find a suitable gaming laptop for about the price of the PC I linked, give or take.
Whatever you're looking for, please let me know your budget and any other considerations, for example if you'd like extra storage. Please also let me know whether you'd like the best system your budget can get, or the cheapest good system that will meet the requirements you're describing.