Good to hear you got your connection stable, if things stop working in future (especially if you haven't made circuit changes) remember that it could be that connection getting flaky again. If possible keep the small circuit you used to test it around so you can verify it is still working in future and your problem hasn't come back as it can save frustrating hours searching for a problem that isn't in your circuit but in that connection 
. As to breadboards, yep looks like you have one of the half (around 400 pin against 800 for the one in breadboard) breadboards. You'll need at least a full size one to get just the buttons and leds you currently have in your first circuit on to it. You may want to get something like this (most local places will have them) or just some 22 or 24 gauge solid insulated wire and cut and strip your own to make smaller jumpers at least for things like the ground connections. The flexable wires with pins that you look to be using are good for longer connections or ones that you want to change often but they get crowded fast when there are many connections. Wires right down on the base of the breadboard will give you room to actually push the switches which looks somewhat difficult right now
http://www.rpelectronics.com/mb-910-breadboard-wiring-kit-350-pcs.html
Peter