Yep, quilting is much more difficult then it looks at first! Going slowly and getting your cutting down right and that pesky 1/4" just right will definitely pay off in the end! If you can alter the speed of your sewing machine to a slower speed, you can still put the pedal down but not be going so fast that your seams get messed up.
Chain piecing feels weird at first, but it will save you so much thread, you would not believe! If you have some cut squares by your machine, you can use them for "leaders/enders" by chain sewing them at the end of your chain, stop with the needle down in the square, snip off the rest of your chain - eliminates thread tails and helps to keep your triangle points from disappearing into the needle hole. You get the added benefit of making two-patches to make into anything you'd like.
Also, if you make a sample block out of scraps with every quilt you make, you will quickly have a sampler quilt as a bonus!