you only need a few pointers, advice goes the same with laptops as it does with desktops.
cpu = brain power, the cheaper the chip, the slower the brain overall works, so all will be slow or slower, add it a cut down one which is a power saving one into the mix in a laptop, and this is double the issue.
memory, more is always better, with less being worse, so simple, 32 bit o/s doesn't need more than 4gb in total, so base mem + vga mem = total 4gb
desktop / laptop, 64 bit, 8gb is great, 4 gb is way too tight, and this is total ram, so base + vga, and rule applies, more = better
so 8gb with a 1gb vga, = 9gb total, which is better than a 8gb laptop which shares 4gb with video, which is bad, or poor to poorer to say the least.
won't mention onboard video, as tbh, if your budget is too low for a 1gb card, then i wouldn't buy one, desktop or laptop, same rule applies
now storage, laptops default to a 5400 HDD, so power saving and rather slooooow
desktops default to a 7200 HDD, again old tech, but ok ish, add in a SSD a solid state drive, or even a SSHD, a hybrid HDD and SSD combo, and it's better than either a 5400, or a standard 7200 HDD, with only a pure SSD being faster, but costing more for a good size drive.
regarding screen size, as once bought it can't be altered in laptops, the biggest and cut corners elsewhere, makes it heavier and also less portable, but well worth it.
if budget is really tight, don't cut cpu, memory or storage, as you can always plug into a larger monitor at home, and make it a desktop once there :)