Bathroom fan, light, heater

I went to replace an old 4', four tube, flush mount florescent fixture in the kitchen and discovered that whomever installed it did not event mount a junction box. Just poked a hole in the drywall and ran the 14/3 into the fixture. The ground wire was haphazardly wrapped around a shard of the knockout metal. Furthermore the wires are slightly burned and cracked. Needless to say I'm going to pull some new romex for this circuit and install a junction box before installing the new light. I've pulled plenty of romex in new installations but have never done a retrofit/replacement type deal. The run distance is very short, as in ~10' or so. I can touch the wall switch with one hand and the light fixture with the other. I would really rather not have to crawl up in the attic amongst the big piles of blown in insulation to fish a new wire from switch to fixture. Is it better to hook the new romex to the end of the old romex and pull the new wire that way? Or hook my fish tape to the old romex, pull the old romex out and then use the fish tape to pull the new romex? And is it better to pull the wire from the fixture end or from the wall switch end... or does it make much difference? Thanks Wayne

Our "new" house (1924 construction) hosts a hodge-podge of electrical history. I'm starting the process of rectifying it. Not sure how far I'll go on my own, as an electrical novice, but I'm moderately handy, and I can read, and I care about doing it right. I'll get help when it's over my head, but I also want to save money and learn how to do it myself, where I'm able. For starters, as part of our closing agreement, we had a new breaker box installed. Now I'm trying to map the existing circuits and assess the state of all the sockets, switches, wires, etc. We've got some of everything--from knob and tube to modern wiring. We've got ungrounded three prong outlets (ACK!!--code violation!!!), reversed polarity outlets, open sockets, unused/connected/disconnected fuse boxes... you name it! My questions is this: when mapping circuits, how can I test when open wire ends (yep!) and sockets and fuses are hot? (I do have a circuit tester and three-prong tester for the outlets. And I also happen to have a multimeter.) Also, short of throwing in the towel and shelling out the big bucks for an electrician to do the whole job, how much of this--with time and patience--could I sanely think of tackling on my own? Can jobs like updating wiring and running ground wires be done--with time, patience, and some research--as DIY projects?