This would be extremely ambitious for a first applique project, even without a pieced background. While I hate to be discouraging, what you describe would be fairly difficult even for an experienced quilter.

If you really want a baseball quilt, I would advise the following: -- plain material for the background. Don't starch it, or starch only lightly on the back of the fabric. Cut it about 2" bigger all around than your final size. Dampen it and press it on a very flat surface (table with a folded wool blanket or towel) - don't move the iron, just steam and press lightly. Do this just before you mark it so that there is minimal risk of distortion. -- lightly starch your foreground fabrics (if using a spray, apply it to the back of the fabric), allow to air-dry on the flat if you can, and steam press when almost dry.
-- for large shapes (jersey base colour, for example), draw them on the front of the fabric at finished size and add seam allowance as you cut.
-- if your shapes are small (logos, letters), make a card template, mark this on the back of the fabric, cut the shape out and glue the seam allowance down with starch or washable glue. Allow to dry then press. -- using a washable marker (I like to use watercolour pencils), mark your design outline on the background fabric. -- place your first design piece onto the background fabric, and fix in place with dots of washable glue. Once it's dry, baste it about 3/8" to 1/2" inch inside the marked line. You can also turn the seam allowance under and glue-dot in place if you think it likely to unravel as you handle it (avoid gluing the turned edges, where you will be stitching) -- stitch the fabric down, making sure that the marked line is on the underside of the fold. -- repeat for your smaller pieces, building up the picture as you go. For the small pieces basted around card, leave them like that until you are ready to use them, then remove the card, baste (glue or thread) and stitch.

As you can probably tell, the aim with hand applique is to minimise the risk of distortion without making the fabric too stiff to stitch through. Thread basting is strongly recommended for large pieces because glue dots tend to come undone as the fabric is flexed and folded during the stitching process.

Good luck (and don't forget to post a photo when you're done - I'd love to see how it turns out!).