Sketchup needs processor power and 3D rendering, so a good processor i5 or i7 combined with a graphics card ( nvidia 2gb for instance ), not on-board graphics chip ( intel 4000 or intel 4400, not good enough ) and at least 4gb ( better 8gb + )ram will let you design a detailed house. If you just want to design furniture and basic designs then almost any laptop will do as long as it has 4gb of ram. More power means less battery, Its the trade you have to make. Obviously the more you pay the better the machine and the longer the battery life, buy a battery bank and work for hours, usb mouse with its own battery, turn down the brightness a bit, don't use touch screen, turn of windows aero just while you are designing, all these things would help but a good graphics dedicated laptop is best
my laptop Hp envy win10, i5 2.2GHz, 8gb ram,intel 4400 graphics and will struggle on a large design once the 3D gets heavy as the processor is doing everthing, and being a touchscreen windows 10 makes no difference. I can't make it better so remember that the laptop you buy is the same in five years, so go big.
My pc is a cheap dell, Win7, i3 2.93 Ghz, 8gb ram, NVIDIA GT 4300 (1gb nothing special) is much better. I use two screens but the Graphics card is doing the 3D work not the cpu so rotating, zooming and moving around the design are much better, it will still glitch for a second or two sometimes but has never crashed or frozen for longer, A better graphics card ( cheap example Club 3D GeForce GT 640 Graphics Card - 4GB $100 ) and i would have not issues.
I am in the UK so can't comment on prices but the more you pay the more you get, I would expect to pay around £700 pounds and upwards from there. so $850 dollars to start.
Hope this helps