You can applique anything on anything just so long as you use the appropriate stabilizers, fabrics and technique pertaining to the project at hand. The choilce of sewing machine is unimportant as you can do it by hand if you want. Indeed, bequtiful work was done by hand for years before the machine was even invented. The raw edges were turned under and stitched down with either tiny almost invisible stitches or a decorative hand stitch.
For a T shirt, I would first use a light weight mesh iron-on interfacing on the wrong side of the shirt. I would use light weight fusible on the applique but more crisp, not mesh.. Use a few dots of fabric adhesive to hold this in place. You can then sew carefully around the app. (or hand baste) making sure that it does not bunch and finish with a zig-zag, satin or a decorative stitch. There is a blanket stitch on your machine which would give it a rustic look. Use either a matching thread or contrasting/ fancy thread to achieve the look you want. If you want to tuck the raw edges under rather than cover them, you can finish with tiny, hand worked running or whip stitches. There are some good nylon invisible threads around which come in white or dark. Do not use monofilament (fishing line thread) it is nasty stuff.
Ladysmith BC,Janome 12000, Bernina Record, Bernina 1150MDA serger, bit of a Luddite, garments not crafts
To be honest t-shirts may be a bit hard for first timer, as the material will stretch.
I'd try a cotton on cotton first. you can buy a product that allows you to iron the applique straight onto the base fabric, which will stop it moving and make life a lot easier. then you satin stitch over the edge using your machine, although jaquie does have some good ideas to make it fancy!
the only place housework comes before sewing is in the dictionary janome 8000, 9000 and just about every card ever made!