You dont need a 4k dollar laptop to run EU, but a dedicated gfx card is important.
Over 3yrs ago I got this one,
http://www.amazon.com/gp/product/B004G5ZXH0/ref=wms_ohs_product?ie=UTF8&psc=1
for around 6-700 dollars and have been using it for work and EU ever since.
I have been starting to get slow startup times in the game and excessive timeouts along with my internet browsers freezing from time to time. Basicly its been 3 years and is due a new one, but I cant afford one this year, so I purchased a SSD for it for ~120$ and reinstalled windows. It has run much much better since then with EU starting normaly again for me and I just counted I have 4 separate Internet browsers running with a total of ~40 tabs, none of which 'hang' or 'freeze' on me anymore.
For another $100 I also ordered 8gig of ram (up from the 4 it came with) and a new keyboard (after 3 years of constant use i am missing a few keys and a few others stick, most annoying of which is the Spacebar)
I am playing with medium to high settings for most everything.
My point is you dont need an expensive computer to run EU... you need a dedicated gfx card.
Look for the cheapest you can get that has a dedicated card, i5, and 8gig of ram and you should be ok.
I was surprised at the difference the SSD made, but some of that can also be attributed to a fresh windows install. You can add that later fairly cheaply if needed.