Prepare the Crust: Preheat your oven to 325°F (160°C). In a bowl, combine the graham cracker crumbs, melted butter, and 1/4 cup sugar. Press the mixture firmly into the bottom of a 9-inch springform pan.
Make the Filling: In a large mixing bowl, beat the cream cheese until smooth. Gradually add the remaining sugar, vanilla extract, and mix until combined. Add the eggs one at a time, mixing well after each addition. Finally, stir in the sour cream until smooth.
Bake the Cheesecake: Pour the cream cheese filling over the crust in the springform pan. Bake for 45-50 minutes or until the center is set but still slightly jiggly. Turn off the oven and leave the cheesecake inside for an additional hour.
Cool and Chill: Remove the cheesecake from the oven and let it cool at room temperature. Once cooled, refrigerate for at least 4 hours or overnight.
Prepare the Topping: In a bowl, toss the fresh berries and peach slices with lemon juice. Top the chilled cheesecake with the fruit mixture just before serving.
Serve: Release the cheesecake from the springform pan, slice, and enjoy your delicious berry and peach cheesecake!