Hi Stepahnie,
I've been on the patch myself for about 3 months now. I discussed all 3 options with my doctor before starting and we both agreed that the patch was the best choice for me.
My understanding is that if you can manage to take the oral tablets sublingually (dissolved under the tongue rather than swallowed), then they should have similar risks to the other forms, but swallowing them partially or entirely can put a little more strain on the liver, and may further increase the risk of blood clots.
Between the patch and the injections, the patch provides a steadier dosage, and might result in fewer mood swings, headaches, and other symptoms of hormone fluctuations.
I've not had any trouble with the patches coming off, even when showering and scrubbing the area, but different manufacturers' patches may vary in how well they stay on.
I usually wear mine a bit above the waist, and I don't generally go anywhere topless (not that I could at this point!), so I've not had any privacy issues.
Your mileage can and likely will vary on this (I'm in my 30s), but if you're concerned about changing at the gym, or being seen in swimwear, etc., keep in mind that regardless of what format you use, at some point you will likely have other things that would out you, or at least raise some questions, and possibly sooner than you think

-Megan