What should I look for in a laptop?

I guess I'm getting to where I'm becoming a bit more on the move than I used to be, and my tablet isn't cutting it anymore to run my basic operations I would need to use.

I'm basicly looking to get a side-computer to help me on the go, but not to take the place of my workhorse "Gaming" Desktop.

I'm looking for a windows Laptop or possibly tablet that can last me for the next few years from my upcoming senior year on through collage. I mostly would need it for basic office functions like word and excel, and lighter music applications like Fender Fuse for my amplifier. The maximum load I would like to put on it is maybe a older game like skyrim on lower settings.

So i need help figuring out how much computer power I need to pay for... I know for sure I don't need an Alienware or an overclocked i7, but I know an average chrome book won't do it at all.

Is this about spot on?

CPU: ~intel i3 4th gen or greater (this is where I am shakey)(I can upgrade later right?)
RAM: 4GB+
HDD: 600gb+
Battery life: ~7 hours (BTW my old laptop is about 15min now)
Size: 14-16"
Ports: USB 2.0, HDMI, Ethernet port, DVD drive, headphone jack, yadayada

What are your opinions on the power needs for a basic everyday laptop computer?

Suggestions are appreciated as well.

I have been using my Desktop build for so long now I have forgotten how much power I really need to get along, Haha