What are the specs of the computer that will fit my needs?

I decided that I want to get a Windows laptop, but I'm not sure about the specs that would be appropriate for what I'm trying to do. I want to make a backup of over 32GB of files I have on my flash drive and copy them onto my computer. I will be working mostly with Adobe programs like Photoshop, Illustrator, InDesign, and After Effects (and they take up a lot of room). I'm gonna have a few additional free programs installed, but aside from that, that's all I need my computer for. I won't be doing any games or anything.

I just need to get an idea of what to prepare myself for. I've had so many problems with my last two for such a long time and I don't know why. This time, I want everything to go straight. So what are the specs of a greatly functioning computer that will allow me to do these things? Please be as specific as possible.

Added (1). The price doesn't madder. I just need something that works.

Start here:
http://blog.laptopmag.com/best-worst-laptop-brands-2014/3
I would not consider anything other than a Lenovo, Asus, HP,. Or Samsung (in that order)
WRT Lenovo's all of their machines are great but steer clear of their Essentials line. Those are the most basic. WRT HP, I don't encourage their consumer grade machines but their business class machines are beyond reproach (Elitebook, ProBook, Envy).

For your described needs, you will do fine with Integrated graphics. You should consider a machine with an i7-4xxxM/MQ/HQ processor. Do not get one that ends in 'U' - those are designed for ultrabooks and will not have the horsepower you will want. Get at least 8 gigs of RAM.

Other than that, purchasing a laptop is a highly personal decision. You need to decide what type of keyboard you want: do you want a full sized keyboard or are you okay with something smaller? Do you like or despise the chicklet keyboards like apple uses? Do you want a backlit keyboard? Do you want a numeric keypad? Do you want a touchpad and/or point stick? Do you want 2 mouse buttons or 3? Do you want them above or below the touchpad? How large a screen: 13"? 14"? 15.6"? 17"? If you are highly mobile, then smaller is lighter. If you don't move around much then bigger means heavier but a much more visible screen. These things and more are all things to ponder which will have a significant impact on how happy you are with your laptop experience.

It ultimately depends on your budget. If you tell us that I can give you more specific recommendations. However, if you're using Adobe programs it would be best if you get a computer with a dedicated graphics card.