( i’ve moved this to projects so you can get individualized answers based on your own needs and preferences. 
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You don’t need a computer. The combination of the smartthings hub plus the SmartThings cloud provides the processing required. You do need a apple or android smartphone and a 24/7 internet connection for many of the home automation features.
Hub Model
At this point, for security the only smartthings option I could personally recommend is the smartthings/ADT security panel model. There are no long-term contracts – – you can pay for the ADT central station monitoring feature on a month by month basis. If you follow the links on the SmartThings site to “security” these now all take you to that particular model line. It should be somewhat less expensive than what you were paying now, but it’s not super cheap. But it should be much more reliable than most of the super cheap options.
In particular, it is the only smartthings model line which has cellular backup for communication with the central monitoring station. All of the other model lines rely on Internet notifications.
https://www.smartthings.com/home-security
It’s also the only model line which can contact the central monitoring station for smoke alarms.
Ecobee
The ecobee will work fine with SmartThings, there is an official integration as well as some third-party apps you can consider to add more functionality.
Zwave switches
Most of the Z wave switches can be reset and then just added to SmartThings. If you give us the exact model numbers we can say more. Some of the multi button scene controllers may not transfer easily.
Security Sensors
Honeywell separates its devices into different categories, with “security” devices being different from “Z wave” devices. The important thing to note is that the security sensors are using a proprietary communications protocol, and will not be able to work with smart things.
This type of architecture is pretty common in security systems, and in fact the ADT/SmartThings model line has its own set of dual logo security sensors which also use a proprietary communications protocol, not Z wave. Only the dual logo sensors can be used to trigger an alarm to the central monitoring station.
(Z wave is a good protocol for lighting systems, but it’s just not quite a good match for security for some complex technical reasons including the fact that there’s no enforced sequencing.)
Other Factors
I’m tired today, so I don’t want to go into a lot of details about reliability, but you should read the following FAQ (this is a clickable link):