Agree with Countess.
120 staff is unusually large to have no internal HR presence. We find that once businesses get to about 50 or 60 staff they are usually then at the stage they need someone in-house. Sometimes sooner.
If they are going to appoint someone internally, an experienced HR Manager would be best, to set everything up, assess current practice/culture/procedures/issues and use his/her expertise and experience to do the necessary ‘catching up’ required. At that size of business, there will be inconsistencies, vulnerabilities and issues that will have crept in, no doubt.
If they don’t want to appoint a full time/part time HR Manager, they could either outsource it to a consultancy specialising in SMEs, or they could do a combination, where they have an internal lower-level person who is responsible for HR admin (there probably is someone already, possibly an office manager-type, that’s really common) but that person is able to access advice from an experienced professional externally.
From your own point of view, if you want to move into a career in HR, by far the most sensible thing to do is to look for work in an HR department in a bigger organisation, so that you can learn and observe how the function works, learn from more experienced professionals, learn about the annual cycle, learn about the various areas of work established HR departments deal with. You are not going to get any of that working on your own in an organisation without any current HR.