I semi agree with the purchase of a H.O. alternator for SQ. Really not needed. Big three and a good battery will be a better investment for an "SQ" system. Also, a power supply for tuning but, that's later. If you do not plan to run your vehicle off for long periods of time or pushing some crazy 10K amplifier then you should be good.
I know my thought process of building a system varies from car to car. Is the new car a virgin?
With a clean slate I would suggest figuring out your source unit. This alone can take you some time researching and reading the internet on reviews and talking to people. Single Din, Double Din, OEM or Tablet. There are a bunch of ways to go now a days. In the end it comes down to personal preference and features. Personally I am an Alpine fan.
Speakers and Amplification go hand in hand. Unfortunately, not all shops have a sound room and even if they do it is not always the best way to judge a speaker. What sounds good on a wall does not always sound good in a car. The best way to listen to a speaker (IMHO) is in the vehicle. I would suggest to find some SQ shows and get some ears on. This may be a difficult task and will take you some time so be patient. It is worth the wait.
However, the biggest improvement you can do is add a subwoofer. This would be 2nd or 3rd thing I would do while you get you gather your thoughts and equipment. Just a 100-500 watt amp, sub and pre fab box.
Not sure if this was any help, good luck.