It is normal to take up to three months to adjust to a new type of pill. This is true for the NuvaRing as well. Staining is common during this initial adjustment period but usually subsides at that point.
We do not recommend trying to skip the week of placebos (or in the case of the NuvaRing the week without the ring) during the initial adjustment period since it likely will cause more staining. Once you have adjusted to the pill, then we suggest slowly building up to longer stretches of taking active pills (e.g., try 4 weeks of active pills and then a week of placebos, then try 5 weeks and then the placebos, then 6, etc.). While some women are able to manage three months in a row of active pills, many women will experience staining sooner and should just take the week of placebos to allow a period to come if the staining doesn't subside.
The NuvaRing is a good option for birth control, but may be somewhat more expensive if you plan on trying to extend your cycle. Once you have adjusted to the NuvaRing you can try using two rings in a row without the week off. However, if you start staining and it doesn't subside, you should remove and discard the second ring even if it wasn't used for the full 3 weeks. It cannot be reused after the 7-day break; you will need to insert a new ring. This is in contrast to pills, where you can skip the placebos and start a second pack, and if you start staining and take the 7 days of placebos, you can continue afterwards with the unused active pills left in the second pack.
Whatever you decide, please make sure you are familiar with the laws of stains so you can avoid becoming niddah unnecessarily.
Please feel free to get back to us with any further questions.
B'hatzlacha!