There are a number of good books on machine quilting. Harriet Hargrave's is really good, and I have another "Bible" called Quilting in Sections. Hargrave says to use masking tape all around your backing.
With your Trip around the World quilt, I think going diagonally is best. Use the walking foot and don't pull or push. Just let the machine move on its own while you hold the quilt flat. Start at one corner and work your way to the other. You may need to put up with a few puckers at first. After the quilt is washed, they may not show anyway.
Are you using cotton batting with cotton back? Some people swear you need to use cotton thread, too, but some don't. It takes practice. Don't be too critical - you will get the hang of it after a while.