Gilrucht, your question implies your answer because you are using the language of spreadsheets. Not surprising, since you are also using spreadsheets. Why WOULDN'T you use their language?
However, the issue with spreadsheets is GROWTH. You are describing a small business enterprise. To be honest, a spreadsheet is perfect for very small businesses. But if you ever want to grow, spreadsheets will be limiting.
When you use language such as "we will never want to do..." - odds are you will find a need within 6 months. (Murphy's law in action.)
I'll toss one your way. In the USA, a spreadsheet probably doesn't meet the requirements of HIPAA regarding security of patient records. OK, maybe you don't care about that - but someone does.
Let me give you some very important advice. Learn to do regular, almost excruciatingly regular, backups. Spreadsheets are an all-or-nothing-at-all thing. If you lost the sheet, you lost it all. Databases can be more easily repaired. There are ways to devise archives.
In general, the greater flexibility for RECORD management lies with Access. The greater flexibility with data ALTERATION lies with Excel.