The minimum points to convert are 10K. You can convert any number of points, but they must be in increments of 1K. For example, if all you had was 15K Avion points (the welcome bonus), you would score 22.5K Avios points. That's enough for a flight from Toronto to Miami direct--and depending on when you wish to go, you could score enough tickets for your family, but be warned, availability during peak seasons is non-existent. Also, flight availability with routes that used to be plentiful have dried up, in some cases, TOTALLY. You used to be able to get plenty of flights per day through your Avios points to fly American Airlines from Toronto to LaGuardia--no longer. Now you cannot find a single seat, whether flying business class or economy.
First, AA forced British Airways to increase the number of points it took to fly short haul flights in North America, as their rates were better than anyones, including American. Then, they stopped supplying them with flights to NY, and likely to many other places.
I've basically given up on Avios points personally. I'll throw some points in with my AMEX to Avios to keep my account (and my wife's) alive, and sell my Avion points. It's worth more in cash now with the conversion than before. But check to see if the routes you want are even available with Avios points--if so, this is the time to convert your points!