This winter I got a new job and my commute went from 54 miles each way to 6.
I decided that the thousands of dollars I'm saving in gas was a good reason to buy a new bike. So now I want to set my old bike up to start riding to work at least a couple times a week.
The bike in question is a '96 mongoose omega. What changes would be the most practical to start with?

Good for you, that is great! 6 miles is my commute distance too, you will really like it. I am full-time commuting by bike now, although 5-for-5 weeks are rare due to my job having lots of business travel and overnight stays, etc. I don't know much about the mongoose you mention, but I will suggest fenders (if your bike will fit them, some won't), a rear rack (if your bike will fit them), and good waterproof panniers for the rear rack. If you can afford Ortlieb classic backrollers, you will love them every day you commute. Good luck, and good move... you will love the 6 mile commute.

also the tires if you got nobbies/ mtn bike tires get rid of them. Get you a set of street slicks for your size wheel it will make your bike faster and easy to handle . Igot a set of trekking bars ordered for my bike plus if you wear a helmet good idea to. Get a helmet mirror so you can see what is coming up behind u not required but always good to have. Also a good set of lights front and back. I would also consider either thorn proof tubes or tire liners your choice cause of broken bottles or nails. Good cheap insurance ... but I think you will do fine..

I'll second that 'good for you!'. You'll love it.

My commute happens to be six miles, one way, too. It's a great distance; not too short and not too long.

I'm not familiar with your bike, either. But I imagine it's a basic mountain bike and that's just right for the task.

In a nutshell, you want to be prepared for bad weather. The reason is that if you don't, then you'll not be able to ride the first time there's any chance of rain. And then you'll hardly ever ride. So you want fenders. Figure on about $25 (and up) for them. Another $25 for a rear rack. I use two (one on front) to be sure that I've got enough cargo carrying ability. I carry my stuff in a couple of medium sized (maybe 30 inch long) duffel bags that I get from the Beast of Bentonville for about $15 each. I give them a coat of Camp-Dri. And if it's really wet out there, then I put them in garbage sacks and strap 'em down. My stuff stays dry even in the worst weather.

I advise two mirrors; one on each handlebar. Most cars will be more courteous to you than you might think from our ranting. But there's some fool every here and there who will come too close and not even try to make a little space. You want to be able to watch these guys as they approach.

Tires depends somewhat on what you expect to ride on. I run near-slicks during the definite dry season. But this time of year I run on knobbies. If you're sure that you'll never be riding on that half-gravel/half-dirt stuff on the side of the road, then maybe you don't need knobbies.

For rain gear I buy very basic two piece rain suits. I leave one set as is for colder weather. The other set I cut off the arms at the shoulders and the pants at the knees for warmer weather.

Come on in and join us. You'll never regret it.

Thanks for the advice. From what I've been able to dig up, the bike was some attempt by Mongoose to get into the cross market.
i normally ride 700x23 but I can fit up to 32 on my frame so I went with some "city" tires that aren't real knobby but have a bit more tread than my road tires.
i hadn't looked for fenders or rain gear yet but I'll look into those.
Mirrors didn't even occur to me so thanks for bringing that up.
I'm assuming I'll figure out what works for me as I go, but these seem like good places to start.

As noted, racks and panniers to carry the load.

Rain gear -- fenders are great, jacket.

Lights for rain, dark, fog.

Unless you work odd hours, you won't need lights until Fall.

I would concentrate on storage and visibility first. That means a rack and panniers or a backpack, and a brightly colored top.

I used a backpack at first but got tired with my back being sweaty all the time. Panniers are much nicer, but expect to spend about $100 for the rack and some basic bags.

For the top, I went to Home Depot and got a construction vest for $10. It looks silly, but it does the job. The reflective strips are nice when it's foggy or generally gray.

After you ride for a bit, you'll get a better idea of what's needed and what's not.