I think the key issue here is security which you hit on in your first post.
Many platforms support SSL so that shouldn't be a problem but, setting up a remove application to fit your business requirements may be.
If you purchased a VPS(virtual private server) or a dedicated server you could likely access it through RDP(remote desktop) giving you a friendly development environment without having to deal with too much security. The drawback here is that both implantation tend to be rather pricey depending on the demands of the application. (disk space, CPU power, ram, open connections, speed...)
It also puts everything "out of hand" as far as the hardware goes... Not sure if it will ever be an issue but, for example we have had hurricanes and various other things knock out power for our server hosted in TX. Although they did have backup generators we had down time. (wasted time = wasted money)
I have also heard of raid clusters corrupting and causing issues... To shorten up my last few examples, if you are hosting any valuable or sensitive information you will need to have backups as well. This is usually provided by the hosting company but once again digs into your pocket.
I am also not sure how you would pass the commands back to the local computers to execute or if the business itself is even comfortable hosting the information off site.
The second alternative although far more pricey and work to set up initially would be to build the server yourself on site then set up the network for remote access.
This however opens up security holes(network would need to be carefully set up) as well as the need for a technician if things go bad. It would however give you direct access to run commands as well as the advantage of everything being local if you ran into problems.
If it's just for a small business I would probably go with a VPS, they are generally more than enough for moderate traffic and demands.
Everything is situation and there is truly no correct answer. Your preference is really what it comes down to... To be honest, anyone in the computer world knows you will likely be the one called when/if things go south.