Arq does not have bootable backups. It is primarily for long term off site versioned backups. Look at SuperDuper or CCC for a full metal bootable backup.
I generally prefer SuperDuper for its simplicity, and recommend it to most people.
CCC is not really harder to use, but presents a bunch more options which most people don't need and with which they may get into trouble. One great feature of CCC is the ability to do bootable backup to a remote volume. I have my MacBook set up to backup to a server in this fashion. However, this requires you to configure your remote server with root SSH access via certificates.
Thanks for pointing out CCC's ability to do a bootable backup to a remote volume. I've had the question on how to do that many times and it is one of those things that is hard to google for when you're not sure how to ask.
I pine for a Mac backup service that would let me backup from anywhere, and in the event of failure, I could fire up a new Mac, point it at the service, and boot to restore all over the net.
The problem with bootable backups is that you need root access to do the types of low level disk writing required. Thus, you need a very trusted environment.
That said, you can also use CCC and SuperDuper to backup to a disk image file. This would not be directly bootable, but it can be copied to a new hard drive which would then be bootable. Backing up to remote disk images is much slower than the root method to drive method.
I think the advantage of a bootable backup is that it is there, and you can just boot from it (or copy it to an external hard drive if it was on a remote volume). The point is that the backup was already in the right format. I think internet recovery is more about restoring from a time machine backup, which takes forever.
I generally prefer SuperDuper for its simplicity, and recommend it to most people.
CCC is not really harder to use, but presents a bunch more options which most people don't need and with which they may get into trouble. One great feature of CCC is the ability to do bootable backup to a remote volume. I have my MacBook set up to backup to a server in this fashion. However, this requires you to configure your remote server with root SSH access via certificates.