Connecting Output Pins to Project

Looking for advice on the physical connection to use between Arduino Uno output pins and my project. I am using 10 output pins to connect to 10 circuits, each ending in 24-Awg wire. I would like to be able to connect the Arduino securely to the project, but also have the ability to easily disconnect it so I can use it on other projects. The connections also need to be able to handle some movement (the project is a textile wall hanging with integrated LED lights, will be moved around a bit, but not to the extent of a true "wearable"). Right now I am using jumper wires from the pins, then alligator clips to connect to my project, but this is bulky and messy and a pain to connect/disconnect. Appreciate any suggestions! Apologize for such a "basic" question, this is my first project (hopefully first of many more).

Use Dupont connectors.

See:
http://forum.arduino.cc/index.php?action=dlattach;topic=376971.0;attach=153794

Or a screwshield.

How about buying a few more Arduinos? Get smaller ones - Pro Mini or Nano - and solder stuff firmly in place, they normally come with the headers not soldered in yet so you can solder your wires in the openings instead, save more space.

They're cheap; I get mine for approx. USD 1.5-2 equivalent a piece, plus a bit for shipping.