when you use freezer paper- it is normal to leave a turn under amount outside each peice (did you do that? anything from 1/8"-1/4") there are lots of u-tube videos- and tutorials here for needle turn applique-
if you are doing raw edge applique a fusable is usually used instead of freezer paper- no turn under allowance- the pieces are cut out on the lines- then fused into place- then machine stitched down.
machine applique the stitches usually show- needle turn applique they do not- or you can use a blanket stitch if you like the look of the blanket stitches showing- blanket stitch is usually used when working with wools- heavier fabrics with no turn under.
it all depends on how you want your finished project to look- and the products used-
start with checking out some tutorials- videos- and deciding what kind of applique you are doing.