You can only sponsor someone to come to Canada once you're 18. So you'll have to wait at least that long for her to immigrate permanently. You'll be 19 in two years, so that's fine.
You can either get married or live together for a year. Then you apply for sponsorship.
It's true that CIC is sometimes suspicious of relationships that are only over the internet, or weddings without family present. They may have the impression in those cases that the relationship was formed so that one partner could get into Canada.
However, CIC rarely suspects people from developed countries (particularly ones like the U.S. where most of the population is white - that's their track record, unfortunately). So in practice, you're probably safe, and it's better to conduct your relationship as you see fit, rather than do things differently because of hypothetical future immigration problems. If your girlfriend was from a poorer country (or even perhaps a rich Asian one), my advice might be different. Also, I've heard of same-sex couples having problems in this sort of case, or people with a significant age difference, even though one spouse was from the U.S. Generally, people are not entirely protected from the individual biases of visa officers in this process.
One option is as follows. Once you're ready to live together and get married (or get married and live together, if that's your preference), she comes to Canada with visitor status. Even though she may intend to marry you and apply for permanent residence (which she should be honest about with the border officer), as long as she intends to comply with immigration laws (such as not working/studying, leaving when required), she is allowed to enter the country as a visitor with "dual intent." Once married, you can apply to sponsor her. Provide lots of proof of cohabitation, if you can. If you have any problems later, you'll be able to present evidence right up to the time of an interview, so if most of your cohabitation is after you're married, that will be okay at that point.
You'll have two choices about how to apply: "inland" and "outland".
If you apply inland, she can stay with you in Canada until a decision is made. Normally, if your case doesn't raise any suspicions, she can get a work/study permit after about 6 months (this is called "approval in principle"), and in some practical ways has most of the rights of a permanent resident (e.g., in-province tuition in university). It takes about another 8 months after that to get permanent residence. However, if the case raises suspicions, it will be forwarded to a local CIC office, where it can encounter extreme delays, of up to two or three years. In cases like these, "approval in principle" is not granted until the case is finalized, so your girlfriend will have few rights in Canada, other than to live with you. Unfortunately, the decision of whether to grant approval in principle will likely be based only on the evidence you submit in your initial application. So if you have some period of cohabitation at that point, things will be easier.
If you apply outland, you can expect the process to take about 6 to 19 months [correction: 8 to 13 months], depending partly on the visa office in the U.S., partly on your application, and partly on luck. She can stay in Canada with you as a visitor during processing, but cannot work or study. She has to keep renewing her visitor status, and this isn't automatic. If you disagree with the final decision made by CIC on the permanent residence application, it's much easier to appeal an outland refusal than an inland one.
What I've said here doesn't apply in any way to you going to the U.S. to marry her. In that case, if you plan to get married and stay on in the U.S., you have to get a special visa.