The biggest mistake beginners do is too much water/to frequent waterings. When pests/disease appear ask in reddit until you start identifying the problems yourself but if a plant has enough sun, water and soil (don't overcrowd a small pot) and the temperature is correct for it to grow don't expect many problems.
If you don't have enough sunlight for fruits you can start with herbs like basil, parsley and coriander. Cherry tomatoes will probably also work but don't expect a huge harvest without appropriate sunlight. Carrots are a tiny bit harder to grow but I got a few to grow in a pot near a window so it's not impossible but they do like a lot of fertilizer.