There are many different varieties of peach, but the main distinction is between clingstone and freestone. You can use either for this recipe: The peaches will cook down into jam, so how well you cut the fruit or separate it from the pit isn't a concern. To boost the citrusy tartness, try adding a few strips of lemon peel (discard them when you take out the cloves).
Put the sugar, 2 tablespoons of the lemon juice, vanilla and cloves in a heavy, nonreactive skillet. Cook over medium heat, stirring occasionally, until the sugar dissolves, about 5 minutes.
Add the peaches to the skillet and stir once to coat. Raise the heat to medium-high, and bring to a visible simmer. Cook, stirring occasionally, until the mixture is thick and jam-like and the peach pieces are very soft, 15 to 20 minutes, depending on ripeness of the peaches. Check the pan midway, you may need to lower the temperature to medium if the mixture starts to brown.
Crush the peaches with a potato masher, until most of the mixture is smooth and there are only a few chunky pieces left. (The longer the mixture cooks, the thicker the jam will be after it cools.) Remove from the heat, stir in the remaining 2 teaspoons of lemon juice, and let cool before refrigerating. Cool completely in the refrigerator before using. Discard the cloves before serving. The jam will keep in the refrigerator for up to 2 weeks.