I haven't tried sharing files between computers over a direct connection since the LapLink days, so I am a little unsure how to make this work.

My computer has a huge hard drive. My girlfriends computer across the room, does not. Is there a way to safely and securely send files between just these two computers using the wired router they are both hooked up to?

Ideally I would like to just send the files when she needs them, not share folders.

FYI: both computers are Win XP Pro SP2 using a Linksys wired router.

sure is but y'all will need to share folders to be able to transfer.
enable file and printer sharing
same workgroup for each computer
share a folder on each computer
in network places make a new network connection wizard
type in the name of the share, \\*name of share* and follow the prompts.

also get the latest firmware upgrade for your router from linksys web site.

What is the likely hood of this making our computers more "accessible" from the outside?

you're pretty safe behind the router with the latest firmware. i ran a 3 computer network for several years with no problem but was very careful with what i brought into the network.

I also have an AlphaShield "firewall" in front of the router, are they any good?

i'm not familiar with alphashield. here's a not so shiny review.
http://www.cnet.com.au/alphashield-firewall-240054645.htm

I forgot to mention, I got the connections setup a few hours ago and it is working. Thanks.

New thread coming about the router.