If you want to pay the same price for a laptop and a desktop pc, desktops are usually faster.
The keyboard thing is just a thing you have to get used to. After a few weeks/days you propably won't notice it.
Laptops with a 17" screen are usually very expensive.
About archlinux...
It would imo not be the best choice to start with archlinux if you want to use linux.
For the paint and word stuff there are native linux applications like gpaint and openoffice.
But depending on your money you might get a fast pc for gaming stuff and so on and a low price laptop. But question is how good the quality of the laptop is in that case
