SMS-Software needed

Hi Everyone!
I and my team are going to deploy a new service the next month.
I've got stuck with a phone collecting form and literally phone management service.
Here is how it should look like:

1. A customer leaves a phone number on a landing page through a widget of (what service?)
2. We get this phone number and proceed to work with this customer within a platform (like Intercom, for example). The customer receives SMS from our sales manager while a sales manager sends these SMS's through a service (what service?)
   that's all:)

I had thought about the integration of Customer.io + Twilio.com but it failed.
It seems these guys are more about automated campaigns while I need to establish Customer - Sales Team interaction through simple SMS.