It depends on what you currently have. Is it a brand name PC or a home brew? As long as you have a PCI-E x16 slot, which I assume you have, and enough space for a new card along with an adequate power supply it really isn't to bad. It can just be more of a pain in the butt to manage cables in a smaller brand name case. If you have to replace the power supply I'd suggest a modular power supply if you want to make it easy.
It makes all the difference. You can't upgrade laptop graphics card, you are stuck with what you have. Not sure how it will run that game even on low settings. My assumption is your laptop has a lower resolution so it might do a little better. However, it's hard to tell. I believe there is a compatibility test out there somewhere for the game. Not sure if that was part of the beta or not.
mobile gaming is very expensive. I know only a few people who do it and they usually buy a ridiculously over powered laptop for $2,$3,$4 grand just so it is not outdated in a year. You can build a decent gaming PC for $1000ish (PC only).