Planning for Alaska?

Next year, upon graduation, I wish to travel to Alaska for my senior trip. My father has wanted to visit there for 20 years, and I decided that since I just returned from Canada and the weather was nowhere near unmanageable, I could do him a favor and visit Alaska so that he would get an opportunity to finally visit the place he's always wished to. However, I have a few questions pertaining to this:

1) What would be the cheapest way to get there? I live in the southeastern part of the US. Should I fly to Seattle and take a cruise there, or should I just fly straight to Alaska?

2) What places/cities/etc would be the best for touring or visiting for the first time? We will not have a large budget, so keep this in mind when recommending. We would enjoy just being there, so any activities or suggestions are welcomed.

3) What is the minimum budget you would suggest for this trip? Keep in mind that we are from the southeast US, so travel and tour prices should be considered.

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I apologize if this is not the right place to ask questions such as this; I tried checking community rules before posting. Please let me know if you have any advice and/or suggestions! Thanks so much!