Well, whatever sport interest you is an interesting candidate. There is such a wide variety of sports that I'm pretty sure you'll find something that fits your needs! I personally practice martial arts, which is a very good cardio-respiratory activity. Of course, you have a lot of other options. Gyms usually offer lots of group activity for free when you subscribe to them, and most of these activities are specifically aimed at being cardio, like aerobic dance, for example. Actually, any kind of dancing is a good way to get you moving too! It's liberating to dance and it really scores high when wanting to feel feminine! This might be good time to learn a dance that you've always wanted to try (be it hip hop, ballet or tango!).
If you really want a sport that have a high level of cardio implied, (I got my old fitness book out for you) there are the triathlon's jogging, swimming and biking which are sure to do a very good job. You can add to this list rollerblading and cross-country skiing as they also score very high. If this feels like it is too solitary, you can also engage in any amateur league of team sport such as hockey, basketball, baseball... anything that might catch your interest. If you are worried about "not being good enough", just make sure to find a class that is friendly to beginners. Even the best at their sports have been beginners when they started practicing it. Practice is the key to become good in anything!
In the end, the most important factor is that you find a sport that feels right to you. Even sports which are not very cardio like yoga, walking, badminton or tennis are good as long as they get you moving! I have personally tried yoga and was surprised at how the hearth gets pumping after a couple sun salutation and when practicing hard postures. Yoga is also a great sport if you care a lot about keeping a feminine silhouette because while gaining significant endurance, you rarely notice any beefing up in the muscle mass associated with it's regular practice. Same goes for Pilates.
On the issue of your body shape, when you say you are skinny, do you mean underweight? It could be a good thing to take your BMI to see where you are situated. Of course, it isn't the most accurate tool ever designed, but it can give a good idea of what kind weight you should aim for. Methods for calculating your BMI are all over google, shouldn't be hard to find. If you find out that you are underweight, perhaps it would be a good thing to consider eating more healthy calorie rich food, particularly if you plan on starting a very calorie consuming new physical activity.
If you are simply thin and wish to achieve a more feminine shape by gaining some fat reserves, you shouldn't feel bad about trying to achieve that goal, as long as you stay within the healthy range and make sure that you live an active lifestyle, there is no problem with gaining some body fat. However, if it's hard for you to do so, remember that everyone is different and that any body type can be just as feminine as the other. Many girls would probably dream of being "skinny". The most important thing you should focus on is on being and staying healthy and, even more importantly, having fun doing it!
