With the ones I have used you just click around on the homepage selecting what you want on the server and then pay. Some sell second hand repurposed servers on auction that they will set up for you. A while later you get an SSH login on the server and that's it, your server is running somewhere in a basement/bunker/old mine and you can go visit it if you want but in general you can do everything remote. There is even stuff that can let you see the bootup in bios from remote (Called KVM I believe). Some help you set up backups on the server and help you with setting up programs on the server but then it starts to get expensive.
You can also just rent a space to place your own server but I haven't tried that.
Colocation provider will bring the circuits to provide best-path connectivity based on packet destination. There shouldn't be an additional charge for this. They are incentivized to manage their bandwidth so data transfers fast, as they are likely charged wholesale for fiber availability.
You will likely be charged 95th percentile mbps based on your usage. (Again, "pipe space required" to your needs.) Basically, whenever you're busiest -- 4pm-9pm are popular times for us in the USA.
Some customers limit their bandwidth themselves (like, only allow max 12mbps file downloads, etc.) especially when they have the hardware to support huge bandwidth. Or your colocation provider can perhaps limit max connection to 100mbs or 1gbps if you want.
Power is usually leased in amps. If you go over amps the circuit will break -- at worst case scenario. But typically they get in touch with you and tell you to upgrade.
Also, they do want to know vaguely what your service is. Because you'll likely lease their IPs, they will question you if you do a lot of email (caution for spam), or run a Tor exit node (legal hassles for them in many cases).
You can also just rent a space to place your own server but I haven't tried that.