Creating berry cheesecakes is straightforward if you follow these clear steps:

1. Prepare the Crust: In a mixing bowl, combine graham cracker crumbs, melted butter, and ¼ cup granulated sugar. Mix until the crumbs are evenly coated.
2. Press the Crust: Press the mixture into the bottom of a 9-inch springform pan. Use the bottom of a cup to pack it down firmly. Set aside.
3. Preheat Oven: Preheat your oven to 325°F (160°C).
4. Beat Cream Cheese: In a large mixing bowl, beat the cream cheese with an electric mixer until smooth and creamy. This should take about 2-3 minutes.
5. Add Sugar and Vanilla: Gradually add the remaining ¾ cup of sugar and vanilla extract. Mix until well combined.
6. Incorporate Eggs: Add the eggs, one at a time, mixing well after each addition. Scrape down the sides of the bowl as needed.
7. Add Sour Cream: Blend in the sour cream and lemon juice until fully incorporated.
8. Fold in Berries: Gently fold in mixed berries, making sure not to overmix to keep the berries intact.
9. Pour into the Pan: Pour the cheesecake batter into the prepared crust in the springform pan.
10. Bake: Place the pan in the preheated oven and bake for approximately 50-60 minutes, or until the center is set and the edges are lightly browned.
11. Cool and Chill: Once baked, turn the oven off and allow the cheesecake to cool in the oven with the door slightly open for about 1 hour. After that, transfer it to the refrigerator and chill for at least 4 hours or overnight.
12. Prepare Topping: Before serving, mix powdered sugar with any remaining crushed berries, if desired.
13. Release the Cheesecake: Carefully run a knife around the edge of the springform pan and release the sides.
14. Garnish: Top with the berry mixture and fresh mint leaves for a lovely presentation.

With these steps, you are well on your way to creating delicious berry cheesecakes.