All you need for the hardware is the ability to attach a camera and microphone (via USB or a 3.5mm jack), a keyboard, a mouse and an Internet connection. And the video needs to be able to show the resolution you want to vlog on (like 800×600 or 1920×1080).
I recommend a custom PC for everything, because your needs will always change and a custom machine can change with you. It’s a bigger investment up front, but you’ll really appreciate it if you go from a simple vlog to streaming and interacting with viewers. A chromebook can vlog, but you might need a monitor for what you’re showing people, a monitor for the live chat, a monitor for your live production suite, CPU and GPU that can handle all those things at once without lagging, an upgraded NIC, lighting controls, and anything else you want to integrate into your show.
Start with a well organized case and a cutting edge motherboard, fill it with only what you need now, and it shouldn’t cost much more than a mid-range desktop at a big-box store.