You should apply for all nominations that you are eligible. Most high school students can apply to the local congressman and both senators so that is three. It depends on which state you live and how your MOCs do the process. For example in Texas, the two senators coordinate and will not both nominate the same person. There are also service connected nominations for ROTC students, children of veterans, active duty soldiers. There is also 5 nominations for the VP but those are extremely rare but you should apply as well
You are correct, basically you compete on each slate you have a nomination for. After all the slates are resolved, they start looking at the NWL but that competition is much more difficult.