you can get cheap fixed broadband everywhere (mobile - I know there are some solutions, but I never tried "broadband" mobile here, it's not really fast anyway, for mobile I'm only using gprs here, and that's no good for chat).
for maximum 50USD installation incl modem and 20USD/month you should be able to get a good adsl line for your needs, cheaper is also possible. some areas also have cable (TV cable) broadband I think.
don't let her trick you into spending too much on a laptop, she will no doubt try that since you are "rich", but most likely she has no use for a fancy laptop as she won't use it for video editing or 3d games anyway, a few hundred USD is enough.
depending on how well you know her, if you're the curious type, and what your plans for her are, you might consider adding some surveillance software ("spyware"
), so that you can see who else she is chatting and emailing with...speaking on a general basis, without knowing her particularly, you could be surprised...just a thought, since many girls are hedging their options.