For casual target shooting, I would suggest a 4" although other lengths can be fun too.
S&W 686s and 19's are great (I have both) along with a old Ruger Security Six.
Originally, I had a 6" 686, but swapped for a 4". IMO, the 4" is better balanced for casual shooting although a longer barrel might be a bit more accurate.
Just a word of warning. Your mother cannot legally buy the gun for you. She can buy it for herself and let you use it. The BATF is very persnickity about this and dealers are extremely careful.
Actually, depending upon your state laws, your mother could give the gun to you. Federal law just prohibits your purchasing a handgun from a dealer. But again, she must clearly be the purchaser. Don't go into a store and look at the guns and pick out what you want and then have her purchase it. Most dealers will refuse to make a sale like that.
Ken