What do I need to do to run a Minecraft Server as far as hardware goes?

You can search around for minecraft server bandwidth. From some quick searching the general consensus seems to be 2-3 players per 1 Mbps (4 is pushing it). The biggest upload from your server would be chunk data when people are moving around, especially if riding minecarts, or if they have access to flying. If it becomes laggy you could shorten maximum viewing distance in your server.properties.

I know that when I checked some site to see if I could run a minecraft server with only 650 kbps upload it said 2-3 players max.

You could likely handle about 20-30 people easily. However; the cost of the internet and electricity from running 64 people on a server out of your house constantly like that (as well as the loss of use of your own computer), kinda outweighs the negatives from just purchasing a minecraft server. RIGHT now, you can get 75% off your server hosting at xdawnedx.com/mchost. I would recommend purchasing either the emerald, or the bedrock plan. (Which right now, will cost you about $20.00 for the first month!)