RE: API Integration with salesforce
Unfortunately this is a major integration project, even if from the outside it looks simple.
For integration, realistically the tooling is provided by 3rd parties like scribe, because it is not straight forward. This is the value products like scribe bring, years of experience and problem solving already done for you.
I would seriously challenge the company decision not to use an integration product, it is short-sighted view. You may also be able to get some support with the integration from a 3rd party, that you will need, and is beyond that possible in forums. Otherwise you are very likely going to need some consultancy hours from an integration specialist to get this going, and there are few specialists working with GP integrations now.
This is not to say you can't create your own solution, just I would say from experience you would not be adding value doing it yourselves.
- just my view on it.
Tim