Would need more than onboard graphics for Eve?
Can turn a lot of stuff down in Eve - but they are phasing out DX9 support so you'd need a GPU with DX11. Not sure Eve really fits what the OP is after (can be quite complex and not always something you can dip in and out of) but who knows - as you can start a free trial now and then continue with an alpha clone you don't really have much to lose trying it out.