I have had to set up PM programs at many companies. Mostly old school with a clip board and some printed forms with the items to do down the left edge and columns for checking when the item was done. These lists usually included several hundred individual items on several dozen items of equipment.
When computers came along, I started making those printed forms on the computer, usually with a spreadsheet program, like Excel. Of course, there is no harm in keeping the record in the computer.
With a three person department, I would think a simple system would be the best. A complicated program would be more of a time waster than it would save.
When you make out the checklists, you will have to make lists of items by the frequency of their scheduling. Hourly, daily, weekly, monthly, yearly, etc. You will need to make the daily or weekly list to reflect the items that are due and the ones that are not due should be blacked out or omitted.
A word of caution, I would make it flexible because in almost all of the systems I set up, we later discovered that a lot of the items that the OEM recommended were either not needed or could/should have been done at a different interval than what was recommended in the equipment manual. And you will find others that you will want to add to the program. You don't want to skip any essential items, but if you include too many non-essential ones, people will start skipping them and later they will just skip the whole list because it is not what really needs to be done. In short, keep it real. These lists will dictate the manner in which you make out the daily or weekly lists. In some cases it may be difficult to integrate all the time intervals into one sheet/list and you will need different ones for different time periods.
Another consideration is that people tend to go down a list, from one item to the next. This may not be the most efficient way to accomplish the tasks. You might consider grouping some or all of the items by the manner or in the order in which they will be most easily accomplished. For instance, if an item requires a particular tool, say a grease gun, then you may want to group all the grease fittings into one place on the list. If the machines are widely spread around the area, that single list of grease fittings may need to be split into two or more sub groups. Each situation (company) may be different. Likewise there may be an adjustment that requires particular instruments of special tools to accomplish. These also may be more efficiently performed by grouping them. What I am saying here is to consider the order in which the items appear on the list and tweak it for the best efficiency.