Here what I suggested when I was asked this question:
Start with high visibility low impact on business execution, meaning in terms of changing habits. Usually service desk that is handling customers/users which has high visibility and low impact in the operating model. It can help to have a tools but probably too heavy at this stage. Start manually to see what could work or not and scale up as you have identified most of the mechanisms.
Look at how the customers feedback are handled, users queries and define a minimal service desk. Knowing exactly what a service desk means. For those not in the know, a Customer services or helpdesk.
Thinking about it, why would you consider ITIL in an organisation with not much IT procedures? You could consider how things are running in your company and things not running smoothly, to say the least. From that on, again high visibility and low change impact ,and progress towards more ITIL processes if the intention is to go ITIL. Your customer are actually those in your company and it is best to have an open communication with them and let them know what you want to achieve. You want the people who would ultimately follow your procedures to “buy in”.
At the end ITIL is a framework like may others. Take what could work for your organisation and the results you want to achieve, not because it has to be..
Fail quickly. Succeed incrementally.