A 3 m cage will means lines of about 1 m which will leave you a plane of about 400 mm span.
With modern motors you can get all the power you need but on such a short lines it will also have to be very light to fly at a reasonable speed. Even 10 mph (4.5 m/s) which is
very slow for an RC plane means it will be complete a lap every 1.5 seconds.
In the past I flew many RTP (power down the wires) planes on exactly this sort of line length and believe you me they needed to be light.
For instance this RTP Fairey Gannet is based on a Keil Kraft rubber powered 'balsa and tissue' kit.
It has a wing span of 450 mm and weighs just 52g ready to go with a brushed motor.
You would be hard put to equal that even with a lighter brushless motor but having to include a servo, a speed controller and a radio.
A possibility would be to use a micro indoor type RC plane something like this.
http://www.gearbest.com/other-rc-toy...FQEFwwodjdoHdQ
Disconnect the rudder and simply use a piece of thread from the wing tip to a central pole. It might take a bit of experimenting to find exactly where to attach the thread to get it to work properly.