I seen at Walmart a $249US Laptop, basically a i3 Core, usually 4-6GB Ram, the norm is around 500GB-1TB of storage and using Integrated Graphics. Photoshop will work on any such low end 'entry level' computer but the problems come out as follows:
It is VERY slow to work with, the HDD is usually 5400RPM which takes a while to load and the IG is not made for 'high end' graphics. It may crash Windows if pushed hard; so you open 10 Websites, working on 5 layers over 3 pictures then you try to open Email POOF! Windows BSOD, why? Because the computer isn't made for that heavy level work, especially a laptop. Go easy on it, don't try to over task the system and you will be fine.
But 1TB isn't enough I work on 200MB files all the time! or That is too low I can't deal with not having at least 50 websites open and work in 50 layers over 12 images at a easy clip! or What do you mean it will take a good ten minutes to load, compile then save one single image! or What do you mean I can't run three 30" displays at the same time!
- IF these or any other concerns are too unacceptable to just live with, then you need to pony it up. Normal Graphics designers use $700US to $1200 machines, usually because they also use two or three external displays which requires alot more horsepower and thus requires you pony up more money.
Intel website tells you, i3 for general (grandma checking email) use, i5 for moderate / gaming use, i7 for heavy work/performance like serious gaming, video editing, large /detailed image editing (photoshop), etc. Video cards also 'step' like that. So if you want to go cheap, then make sure YOUR expectations MEET that level of performance you will ONLY get from that level.