I can recommend banana boxes as they are very strong and can be stacked up too. Don't forget to put your essentials in one box and label it so you can find it asap. Clearly labelling all boxes will help you so much hun, it helped us no end.
As for clothes, this may sound bizarre but are you taking your furniture with you? If you are is there no way of taking your wardrobes/dressers as they are secured with heavy duty tape/ropes so when you get to the new pad you can stick the furniture in the right room and won't have to shift through boxes to find clothes?
Bags are good for soft toys, and other items that don't get damaged too easily.
If you've got time I'd recommend purchasing a roll of bubble wrap off ebay-its cheaper on there and you can wrap are real delicates and put them in a box and label it breakables etc.
If you have any outdated popcorn (the ones you pop in a pan) you can pop them and use them for padding in the boxes for delicates too.
Hope the advice comes in useful.