What is the best Labtop/PC (Preferably all-in-one) to get for minecraft? Budget is $600 or less?

Soon me and my friends are starting some gaming youtube channels and I'm also gonna get a new PC to start playing minecraft again. I want either a labtop so it's easily portable, or a good all in one PC. Any suggestions help a lot, and if you could let me know what fps you think it would run on singleplayer/multiplayer and while recording. Also I've looked at a lot of good PC's but I don't know what the most important specs on one is. So it would help a lot if someone could tell me the most important specs for running minecraft is. (GHz, RAM, etc.) And how many fps a certain spec might get.

Minecraft by itself, you can buy windows dinosaur for 1$ at the dollar store. However, if you stream your game, it'll take a toll on your processor and network. If your internet is ~10MB speed, and in wireless. Just hope no one else is using the internet in the house.

Streaming strains the processor more than your video card. Here's a cheap setup that should perform fine:
4GB ram to ensure plenty of breathing room
duo core i5+ minimum if you get an intel processor on your PC. When streaming, the video has to be encoded before going live on twitch/youtube. Your processor encodes the video for you, while still preserving enough power to run the game and other background processes. If you're gonna stream, invest in obtaining a strong processor over a top grade graphics card.

Video card is the main aspect that affects Framerate.
The newer the card, often times the better. But for minecraft it shouldn't be as impactful. You can identify what video card is newer, ie: GeForce 650 is older than GeForce 660 and thus would run slower with less performance (but that is not always the case, some cards may be older but more powerful) but that holds true most of the time.