I am on the Depo shot but that is because no other birth control method was appropriate for me.
The NuvaRing is a hormonal birth control method, and if used properly it should be over 99% effective.
Here's a break down of what birth controls are and how they work:
There is no universal ''better'' method, as all women react differently to birth control.
There are several types. You'll need to talk to your doctor about what brands and dosages will be best for you.
The birth control pill is a pill taken every day (works best if taken at the same time every day), usually three weeks on, one week off, but you can also take them for three months on, a week off, etc. Discuss this with your doctor. They come in different brands and different hormone levels. The pill tricks your body into thinking it is pregnant by releasing hormones that are present during pregnancy. You stop ovulating, so there is no egg to fertilize, and your cervical mucus also thickens, making if more difficult for sperm to get into the uterus. You can get this for around $20-$50/month from your doctor, or discounted or free from a Planned Parenthood clinic or something similar. Discounted is often around $10 or so.
The birth control shot (Depo-Provera) is an injection either in the arm or buttocks every three months. It packs way heavier side effects than other methods and should be used as a last resort birth control when other methods are not appropriate for the woman using them. It takes a very long time to regulate a natural menstrual cycle and become fertile after using Depo. It also has a heavier side effect of weight loss than the pill, and can lower bone density. That said, you get a shot every three months and forget about it. You don't have to take something daily. Around $40/shot
An IUD is a little plastic or copper T shaped implant, and it is placed inside the uterus. A hormonal IUD releases hormones like the pill would, and also puts a foreign body into the uterus, so if an egg was fertilized it would not implant to the uterine lining because of the hostile environment. The non-hormonal IUD provides a hostile environment. These last 3+ years depending on the type. Some doctors will not give you an IUD until after you've had children, as they have to dilate your cervix to put it in. Around $250
The patch is similar to a Nicorette patch, you place it on the skin and the hormones are absorbed. It works the same way the pill does, but you do not have to take it daily. Change the patch once weekly. Some people find that the patches fall off or irritate sensitive skin. Around $30-$35/month
There is an implant you can get under the skin in your arm called Implanon, and it is 40mm long and 2mm wide, much like a match stick. It releases progesterone only, but again tricks the body into thinking it is pregnant. This lasts around three years but can be removed any time before this. $300 or more to insert, $100 to remove.
A vaginal ring (NuvaRing is a brand) is a thin ring that is inserted into the vagina, where it then dissolves and is absorbed through the skin. It works the same as other hormonal contraceptives, by tricking your body into thinking it is pregnant. Many women I know find that the NuvaRing gives them yeast infections or that they/their partner can feel it. Around $25-$35/month
Plan B (The Morning After Pill) is like the godzilla of birth control pills. It is to be used as an emergency contraception only, and no more than 6 times a year. It is a higher dose of hormones than the regular birth control pill, and if taken properly SHOULD prevent you from ovulating. If you are already pregnant it will NOT kill the fertilized egg or terminate the pregnancy. There is an 'abortion pill' that does this. Plan B can be bought over the counter from your pharmacist for around $40-$80 over the age of 18. Before this it requires a prescription.
Family Planning is a method of birth control for couples that can deal with the consequences of an unplanned pregnancy. This involves avoiding sex the days you ovulate and are most likely to conceive.
The withdrawl method is another method of birth control, though the failure rate is quite high. Despite angry mothers and sex ed teachers preaching, there are NO sperm in pre-ejaculate. No, there are not. Research supports this. The reason is fails is such: 1) The male partner has ejaculated prior to sexual intercourse with his partner, and there are still sperm in the urethra. These can mix with pre-ejaculate, and voila, now you have baby-making pre-com. And 2) guys have lousy timing and don't pull out quickly enough to avoid ejaculating inside their partner. If this is used as a method of birth control it should only be between partners that are able to deal with the consequences of a family (ideally a husband and wife or longterm comitted couple). If you're going to do this, make sure you urinate to clear the urethra of sperm and wash your hands prior to sex, and pull out WELL before you orgasm. Have your partner stimulate you with her hands and/or mouth. The withdrawl method will not protect against STIs. If you combine this (properly) with another birth control method it can be effective.