I have had two laptops recently, all of which played Eve.
An old Gateway gaming laptop with dual hardrives for RAID… it had a gtx 9800, and old gpu, with 512 MB ram. This was maybe 8 years ago. 4 GB system ram, and a dual core AMD processor. it was okay, played Eve fine on low settings, could play one account on high settings, and three accounts at the same time on low. It was a 17 inch monitor IIRC… maybe 15. Any way, it worked… paid 500$ for it. had it a few years and hacked the crap out of it.
Last one was an ASUS Iforget the mdoel, I can look it up if you want, it was a 2014 model IIRC, had 8 GB system ram, a quad core amd with apu, and the gpu was nice, it was a 2GB ram *60 equivelent. like a 960 0r a 560 but it was an ATI gpu. and tbh I hated it. I had driver issues and their support was terrible because I didnt use the newer os that came on the laptop.it was a basic gamers card. This ran Eve the best. I could run 6 accounts on low settings at the same time, but four seemed to work the best. this was a 700$ laptop I got at frys. was a 17 inch.
my best advice, not get a laptop. get a desktop. unless, you are getting this to play Eve on the road like for work or college or military service.
If you do get a laptop, just make sure its a quad core, it should have 8 GB system ram min… and Id say at least 2GB Video Ram as well… a dedicated gpu is a must if you want to run multi accounts or have a smoother experience when gaming.
I think now though, the MSI gamer laptops are decent. The gateway was teh dedicated gamer laptop and that thing was a beast… its just old. it was around 1000$ retail and I think thats where you should look for price point, around there. if you can get a last years model on sale like I did, you may save a couple hundred… the asus was on sale as last years and was a showroom model… it was in good shape, I made out liek a bandit.
Desktop though. if you are gonna play Eve at home, desktop all the way!!!