I have limited funds but electricity is included in my rent. All things considered, what's the cheapest reasonable way that I can get into mining?
Don't bother, you won't make any money mining at this point. GPU mining is dead and you missed out on the ASICs.
You can't GPU mine on a laptop.
Just get one of these.
http://www.ebay.com/itm/HWTOOLS-PM2-V2-1-PCI-E-Mini-PCI-E-adapter-Extend-you-Laptop-to-Anywhere-/170990045076?pt=LH_DefaultDomain_0&hash=item27cfcd0794
Put it in the mini-PCI slot of your laptop, and connect a riser to your full-size pci-e card.
No problemo.