Once you are a registered nurse, you would need additional training to become a pediatric and / or oncology nurse.
Keeping in mind the saying that “a journey of a million steps begins with one”, I would recommend you focus on getting into the best nursing program available to you (US News and World Reports as well as other resources do a good job of ranking college programs, so focus on top nursing programs that meet whatever geographic needs you may have). Top nursing programs usually select candidates based on three criteria:
1) Excellent high schools grades / GPA, especially grades in STEM (Science, Technology, Engineering, and Math) course.
2) Solid standardized test scores (ACT / SAT)
3) Volunteering experience in a healthcare setting (hospitals, hospices, etc.)
If you are lacking in one of these three areas, you can work to strengthen the other two, but use whatever time in school you have left to focus on making all thee areas of your academic profile as strong as possible.
When it comes to paying for your higher education, there are a LOT of scholarship and fellowship programs out there specifically for nursing, and even more for students who are broadly interested in healthcare, so Google is your friend. Also, you can save by taking some of your core courses at a community / 2-year college then transferring those credits to a four year program, but just be sure you have a specific four year program in mind and check with admissions to make sure whenever you're going for your core work is fully transferable.
Best of luck!
Christopher recommends the following next steps: