Good site. I've about re-wired this house. I won't
tell you there's "nothing to it," but I will
say it's not as hard as a lot of people would think. Anything I've done, or considered doing, the least bit unusual, I'd run it by the guys on there to vet.
Geh, a house that old, it's possible that some of that could be knob and tube, although it sounds more like very old romex. I've still got a couple circuits in this house to clean up. Yours may actually be
color coded (black-hot/white-neutral) but I've found that over time apparently the white yellowed and the black faded to a sort of gray so that it can be somewhat hard to tell the diff.
Really though, if it's very accessible (sounds like it is) and for just one circuit, you would save a lot of stress by having an electrician do it. Prices vary around the country, they'll charge more for a circuit, but I should think under $200 anyway. Depending on the distance from the box and some other factors it could be as little as $75. If you have a GFCI breaker installed it'll be more (GFCI breakers typically run $35 or so as opposed to 3-4 bucks for a 15 or 20 amp breaker).
Another possibility if you just want to be safe is installing a GFCI outlet. Your equipment
won't be grounded, but that one outlet (and anything downstream if there is anything) will be safe for you. Such outlets need to be marked "No Equipment Ground."
If you feel like wading through it (you kinda have to be used to the way it's written,) there's an online version of the National Electrical Code to be found HERE.
You can't print the thing but you can reference it.