As this is a more basic phone and does not run android, you may have to move things manually but try this first :
You can try this method of moving your data to the new phone though I am not totally sure it will work as your old phone is am older model.
- Download Motorola Migrate to your Moto G,
- On your Moto G, select "Other" from the first screen in Migrate and then just follow the instructions. This will only work if your old phone has bluetooth.
If that doesn't work and it's names and numbers that you want to keep maybe you could save these to the sim card and put that into your new phone? Photos etc. Could be sent via bluetooth if the phone supports this.
Another way may be to connect the phone to a pc, if it recognises it as a drive you should be able to drag and drop content to your computer and then move it to your new phone using the same method.
The Motorola Moto G is a really good phone for it's class and I think you will be very pleased with your new purchase once it is set up and working to your liking.