 Let's talk stitches.
This is the most important part of applique as this will ensure your projects last the test of time. Just gluing/fusing your applique pieces to your background is great, however, the glue will eventually disappear and your wonderful projects will fall apart.
We don't want that.
The most common stitches used with fusible applique are the zig zag stitch, the blanket stitch, and a straight stitch. If you're just starting out, the best thing to do is to sit in front of your sewing machine and start making some stitch samples.
Get yourself a scrap of material. A plain colour or something you will be able to easily see your stitches on. Using contrasting fabric and thread is a good idea.
Use an open toe applique foot. This foot doesn’t have a metal bar or clear plastic in front of the needle so that you can really see where you’re going as you stitch.
You will want to make a fabric sandwich for your test sample of fabric, stabilizer and fabric. Stabiliser helps to keep your stitches flat and gives extra stability to your project.
Zig Zag Stitch
This is a fairly common stitch, but some machines give more than one option for a zig zag. Depending on the settings of your machine, you can get some very different looks with a zig zag stitch. One will be a satin zig zag and the other will be a narrow zig zag.
Narrow (Fine) Zig Zag
This stitch is not as bold as the satin stitch. Narrow Zig Zag can even be considered invisible. It won’t show up as a solid line of thread, but it will do the job of securing the applique edges. The stitch settings will be a longer stitch length, between .5 and 1.5, and a narrower stitch width, between .7 and 1.5. Again, try out a few different settings and and see what suits you.
Satin Zig Zag
This stitch got its name because it looks like a piece of satin. It is usually made up of very thick and dense zig zags that are so close together you can’t see any background fabric between the stitches. You will want to change the stitch length to .2 – .5 range and the width to 2.0 – 4.0 range. Your design might give you instructions on this. Play around with the settings and see what you like the most.
Easter Applique Flag Pattern
Blanket Stitch
This is a popular method of stitching applique and it’s formed with a straight stitch along the outside edge of the applique followed by a perpendicular stitch into the applique shape. This stitch most closely reflects traditional hand applique stitching. Most machines have more than one option for blanket stitches. Or you might not have any. Test your blanket stitch options on your machine to be sure you have a blanket stitch that is going to have the perpendicular stitch at a right angle to your straight stitch. Some settings can have an angled stitch and that isn't going to work here.
Have a test of the Blanket Stitch and see how you go. You could start with a 2.0 wide and 2.0 long stitch and go up (or down) from there. Depending on personal preference you make like your stitches to be smaller and blend with the applique or larger and make more of a statement.
Easter Applique Flag Pattern
Straight Stitch
This is simple enough and you probably don’t need to make this a part of your stitch sampler. As the name implies it's just straight.
Other stitches
You should have room on your stitch sampler to play with other stitches and their settings. I would recommend you try out a blind hem stitch in case you ever want to try invisible machine applique and maybe some of the decorative stitches like a scalloped satin stitch which could also be used for applique.
 There are lots of stitches you can use in applique, this blog hopefully helps you find the best one for you.