First welcome to the forum and the sport.
There are a few of us shotgun people on here. First please define what you consider “skeet shooting”. Informal pasture clays or actual gun club clay targets? Without knowing that we can’t give you any detailed advice.
I looked up a Mossberg 590A1 Magpul and from the specs I saw, it’s not a good fit for either definition of “skeet shooting”. A 20” fixed cylinder choke barrel with rifle sights will be a significant handicap. Milspec in this part of the sport means nothing. You’re going to want a longer barrel, possibly screw in chokes and bead sights. Shooting a moving target means locking your eyes on the target and letting hand eye coordination do the work. You should see the rib and bead as a blur in the foreground.
If you truly want to try out the clay target games, contact your nearest club. Explain your situation. Ask if they rent guns. Ask if you could have an experienced member mentor you your first trip out. Most likely someone will be happy to introduce you to the sport and get you off on the right foot. If you live, or are going to be in,Manitoba next spring when our club reopens for the summer I will gladly take you myself
As for the rifle stuff, I bow to the members here who have far more experience in that arena than I