First of all, good for you to start making your own gear.
Please know that mittens, especially with a trigger finger might be a challenging first sewing project. They will require sewing around pieces with relatively small radii. Pin carefully and sew slow! You can lift the pressure foot and realign the pieces if you have trouble going around the curves. Here's information about sewing tyvek: the stitch length shouldn't be too short because the needle perforations weaken the fabric. sewing tyvek
If you have never sewn before, you might want to make a stuff sack first, to get some experience operating your machine.
Here's a source for grippy fabric: "Slip Not" fabric
Enjoy the new MYOG adventures and
-Bob home made gear