A few years ago, when I had a <1.5 mile basically commute in SoCal, I picked up a 2002 Trek 4500 hardtail MTB, which I think is similar to yours except for the brakes (rim on mine). It was great for the short commute. Last year I moved to the Seattle area and a 9 mile commute. I got some advice when I posted some time ago on here, and I can summarize what I did to convert my bike from essentially stock to a pretty good commuter. I typically ride ~2 miles to the bus in the mornings, and 8 miles back home in the evenings with a lot of hills.
Lights: I got a Cygolite Metro 500 for the front light. It wasn't cheap, but it works quite well. For the back, I use a Solas Nightrider on my bike, and a Flea 2.0 on my helmet. The great thing about the rechargeable lights is that I can just plug them in at work using a phone charger. I don't see a good reason for reflectors, but I'm sure they won't hurt. I'm not sure extra lights will help. A few lights ensures you are seen pretty well, and 1-2 lights on both front and rear is what I see most people around here using. The one time I was hit was in broad daylight with perfect visibility when someone just didn't look in the bike lane to see if anyone was there. Defensive biking is the only way to avoid getting hit.
Horn: I picked up an Airzound recently, and it's pretty good. A bell won't do anything in traffic.
Barends: I've been slowly looking into this myself, but just have the standard bar for now.
Fork: I replaced my bad suspension fork with a rigid fork a few months ago (Surly suspension corrected fork - ~$90+install for me), and have definitely noticed an improvement. I also noticed that I feel the road more so, but not enough to make a huge difference. But I run my tires at 60psi, so if I dropped them I'd probably make things nicer for myself. Most of my commute is on decent road, with some railroad crossings and the like thrown in. But I recently rode ~5 miles on a gravel/rocky trail currently under development and survived, even with the rigid fork.
Tires: I got Serfas Drifter 1.5" tires and have been very happy with them. No punctures thus far, and they still look good. No issues on wet roads. I haven't tried icy roads.
Fenders: I got Cascadia ATB fenders and have been very happy with them. They block almost all dirt from going more than a few inches above my ankles. I still avoid wearing clothes I don't want to get dirty if the roads are wet - but not much gets on them unless its raining.
Rack: For three miles a backpack is probably fine (or a messenger bag, which was my preference). I realized I needed panniers for anything longer than that though. Since I needed them to function as a bag to bring to the office, take on the bus, and mount on my bike, I got the Topeak MTX DXP bag with one of their super tourist racks. Definitely not cheap, but it made my life much easier since the bag quickly and easily slides on and off the rack.
A lot of my options were somewhat pricier than other available items, but it might give you some ideas