The Bigger the better the faster, the better. Get the best you can afford because it will last longer.
You can still process images on a lower powered laptop/pc it just takes longer. In terms of hardware ram and processor speed are the most important. When you buy a computer make sure you ask how much ram you can upgrade it with. Some mother boards will only take 8gig max, which will be fine for most applications. One of my pc's only takes 8 gigs of ram and is an i5 3ghz and when stacking images using pixinsight it will max out the processor and ram, effectively locking me out of the computer until it's done.
Whether 8GB is enough depends on how big your images are, and how many you want to stack. It doesn't seem enough to do much with 24Mpx frames at 48 bits/px. My next PC will have at least 16G - preferably 32 or 64.
It does not matter if you buy a laptop or desk top. You should however get something with i7 processor, 16gig of RAM or more if you can, a really grunty video card and 7200rpm had drive. In other words just spend big on the system.