reality: a cruel mistress
Welcome to the RTA forum!
The bad news right off the bat: You need to find another plan for a car. No major car rental company will rent to anyone under age 21, except in some very rare circumstances, and when they do, its a minimum extra fee of $50 per day, per under-21 driver.
There are also several other significant issues related to your age, specifically traveling with minors (under 18). Finding motel rooms will be very difficult, because most places will not allow a minor to stay with an unrelated 18 year old. Vegas will be even worse, as you'll need to be at least 21 to do pretty much anything, including renting a room. There are also other significant issues about traveling at age 17, such as you aren't even able to authorize your own medical care, so if you have even a minor accident or injury, there can be big problems.
There's also big problems with the size of your group. 6-8 people really means you need at least 2 cars, and frankly getting that many people to agree on everything, from where to go, where to stay, where to eat, etc is, putting it mildly, a challenge.
All of those things are things you really need to worry about before you can start planning in earnest.
Now, with the details of your plan, I will say that trying to figure a "buy in" figure of $800 is just not a good place to start in your planning. It has nothing to do with the dollar figure, it has everything to do with the approach. There are way too many variables to determine how much your trip is going to cost at this point - it will depend upon all the details, like your transportation, lodging, meals, entertainment, etc and of course the number of people who are going. The total cost per person is going to depend upon how many people are also going to actually go. Realistically, at the very least, you need to get everyone together, figure out who is really serious about the trip, what all of you want to do, and what all of you can actually afford. Even there, things will come up that will force changes.
There are ways that you can do a roadtrip, and go out and have a good time with your friends, but the idea you've proposed involves a mountain of work in front of you. I'd honestly recommend you think about something on a much smaller scale, which is much more likely to go from a dream to a reality.