Depends on the budget. You can get little desktop drawing "tablets" cheap, they're small but work decently. They don't have screens. The best for any art on a computer would probably be something from Wacom, which are somewhat to extremely expensive. They're easier to work on because you draw on the screen itself, allowing you to see exactly where your physical pen will mark the digital workspace, and where to move it to achieve whatever stroke you are making. Other tablet manufacturers are out there that make tablets like this, but Wacom is one of the best brands.
Your question has two major components: Hardware and Software. Whether it's video game art, or comic sketch, there's no difference.
You can go "combo" style and get iPad/Android tablet with pen support. Or (as @Zephyl) mentioned, get stand-alone tablet and connect it to your PC / laptop. If you want just to see how it goes, stand-alone drawing tables won't break the bank.
As for software (in case of PC/Mac) - your options are from free (MS Paint) to $$$ Adobe Creative Suite and beyond.
It depends. If you mean 3D digital art, then a PC is a must. You need raw computational power that you can't get anywhere else.
When it comes to drawing devices. I use a Wacom Bamboo since it runs around $100 and is good enough. If I was going for a something with a screen, I would opt for an off-brand. The Wacom Cintiqs are both expensive and antiquated. They have been surpassed by copy cat brands several years ago. But those will still run you in the $400~800 range.
The main problems with drawing on a screened tablet is the parallax and the heat from the screen. When I first started with digital art I used a mouse and a scanner.