Well, to avoid the transaction being considered "low priority" a fee of 0.0005 BTC would do that. Additionally, if the transaction is larger (greater than 10K bytes) the fee can be higher.
What is 10k bytes in money terms? BTC 1 / 2 / 5 / 10? And how does one check on Bitcoin-Qt the size (in k bytes) of the transaction to be made?
That depends on the quantity and value of the transactions you've received.
When you create a transaction, you spend previously received transactions.
So, if you receive a single transaction valued at 10 BTC, then you can create a transaction that sends 9 BTC and it will use less than 500 bytes. The transaction will have one input (the previously received 10 BTC transaction) and 2 outputs (one for 9 BTC to the address you are sending to, and the other for 1 BTC in "change" that is sent back into your wallet).
On the other hand, if you receive 100 transactions each valued at 0.1 BTC (you still have a total of 10 BTC in your wallet, but now it is split up into 100 separate 0.1 BTC transactions), then creating a transaction that sends 9 BTC will require more than 10 kilobytes. The transaction will have at least 90 inputs (90 of the previously received 0.1 BTC transactions) and at least one output (assigning the total of 9 BTC of value to the address you are sending to).
There is no way to know how big the transaction will be until after Bitcoin-Qt has chosen the previous transactions that it will be spending. Then it tells you if a fee is needed and how much that fee will be.
There are some wallets that have "coin-control". With those wallets, you are able to choose which of the unspent outputs in your wallet you want to use as inputs to the transaction you are creating. This gives you a bit more control over how many outputs are used and therefore over the size of the transaction.
