My $.02:
I went the budget route. I had a small duffle bag (big enough for a pair of shoes and a shirt, I think it was a golf giveaway, though I don’t golf) with a rigid bottom, two side pouches, a front pocket and a padded shoulder strap. It works well for skeet shooting and trips to the pistol range with a soft case inside to hold the pistol. My friend went the same route after being unable to find a decent bag at anything less than astronomical prices. He got a small carry-on style duffle at Walmart for about $10, and added a piece of masonite to reinforce the bottom.
I also have a shooting buddy that uses a small tool bag as a range bag. They are very heavy duty and relatively inexpensive. (Check Home Depot, Lowe’s etc. for these.)
One of these days I may buy a “real” range bag, and the Bagmaster bags look good….