Hypothetically speaking, if a debt free friend were to ask me for my suggestion on how one might safely invest a $10K windfall for a rainy day, I'd alert said friend to the existence of a certain style of bank account that pays bonus interest each month that no withdrawals are made and a token amount (varies between $5 and $200 depending upon the bank) is deposited.
If I was risk averse, a term deposit sounds ideal to me!
If, however, I was determined to risk the money, I would learn as much as possible about investing.
First lesson ... there is a good time and a bad time to enter the market.
Check the chart and ask if this is a good time to buy Telstra (since you mentioned them first)
Second lesson ... learn a lot about a few companies.
Suggestion: Read the TLS Telstra thread (type TLS in the search facility)