I use my power button on my NZXT case to shut down. Can I just go into advance settings and change "shut down " to "hibernate" on the power button?
Yep in power settings, there's an option called something like "choose what power button does".
One thing to bear in mind is that hibernation creates a file on your root drive, i think the size of this file normally is equivalent to the amount of memory you have installed. So this does add additional read/write counts onto your SSD (assuming you're using one).
For web browsers (at least with Chrome and Firefox) you can change it to reload all previous opened tabs, and possibly create a scheduled task to launch the web browser upon you logging in.
Scheduled tasks could be applied to most applications. Although most people tend to go the other way and have as little as possible running on start-up and open what you need after each restart.