I've always been partial to Snapper with their disc-rive, rear-wheel-drive. I currently use an older commercial 21" bagger with Robin engine. Unfortunately something comparable is about $900.

For $450 to $500 you should be able to get a new Snapper mulcher with Briggs engine. Dealer should be willing to replace the mulching cover with a side discharge chute at no charge. Briggs is competent engine, and if you give it reasonable maintenance, should last 10 years in home use. Later on, you can upgrade to bagging chute and bag assembly. Should cost about $200 to make full conversion.