I think I mostly agree with you. Me saying it's a store of wealth is much too basic of a statement in the same way the statement that it's a means of buying things is too basic. You're right; money is a way of converting something into a widely accepted commodity that can then be converted back into something else. My job doesn't want to pay me in cat food, granola bars, and sleeping bags. I do think there's an important storage or accumulation aspect, though. Money lets one take long duration effort and turn it into a very short term purchase (saving to buy a car, for example) or sell a single large item and use the proceeds over a long duration.
First hit for "three functions of money" was at cliffsnotes.com, why not? Store of value. money must hold its value over time ... Money may not even be the best store of value because it depreciates with inflation. However, money is more liquid than most other stores of value because as a medium of exchange, it is readily accepted everywhere. Furthermore, money is an easily transported store of value that is available in a number of convenient denominations. Unit of account. Knowing the value or price of a good, in terms of money, enables both the supplier and the purchaser of the good to make decisions about how much of the good to supply and how much of the good to purchase.Medium of exchange. Without money, all transactions would have to be conducted by barter ... in a barter system, exchange can take place only if there is a double coincidence of wants between two transacting parties.