Since you're only about 3 miles from work, which is actually easy walking distance, my opinion is the bike you have is probably just fine. You probably won't be on it long enough to notice its shortcomings. You can always get a better bike if/when you start riding a lot more than the 6 mile round trip from work. I live in NYC, which means a lot of stopping. I've ridden over 56,000 miles just fine without disk brakes. In fact, I rarely use my brakes at all, but instead just gauge things so I don't need to. For example, if I see a red light two blocks down, I'll stop pedaling then coast down as I approach it. By the time I get to the light it'll just be changing to green while I'm approaching it at 10 or 12 mph, and then I'll accelerate back up to my usual 23 or so mph. I always watch in advance for potential obstacles so as to go around them if the need arises rather than hitting my brakes. Granted, I still need the brakes "just in case", but this "just in case" scenario doesn't really pop up very often. And my rim brakes serve me just fine when it does. I've known lots of riders in NYC who even take their brakes off completely (i.e. the famous cyclists who go through intersections yelling "no brakes, no brakes"). The reason is the as rims get wobbly from constantly hitting potholes rim brakes tend to rub all the time, so these cyclists just take the pads off. Disk brakes definitely have an advantage here, although once my rims get so wobbly that my brakes rub I'll either true them or replace them.
All I'm trying to say is don't fall into the trap a lot of people make when they start riding more, spend a small fortune on equipment, realize it's not for them, then sell it at a fraction of what they paid. I've been riding the same bike for the last 15 or so years. It serves me well even though it has rim brakes, downtube shifters, no shift indexing, no shock absorbers, basically none of the bells and whistles newer bikes have. My only two reasons for buying a new one would be if the frame cracks beyond repair, or if I can buy something significantly faster. The latter is only possible if I buy a recumbent, or especially a faired recumbent. I may even do it one day when finances are better, but for now I'm perfectly happy to ride 10 or 15 miles at a time on the bike I have.
Another thing is if you plan to do most of your riding on pavement look into road bikes. They're a good 5 mph or more faster for a given pedaling effort than mountain bikes. Sometimes that can make all the difference as to whether someone continues riding after they start. Often a lack of forward progress consummate with the exertion put in causes many riders to just give up. A good road bike will definitely help here, especially with a disk rear wheel. A faired recumbent is of course better, but the price tags for those are well into the four figures. Oh, and look into airless tires. I'm planning to get a set as soon as my present tires wear out. Nothing more disheartening than to be all psyched up for a ride, and find your tires flat from a slow leak, or to have a great ride interrupted by getting a flat. Of course, 95% of the time the flat is on the rear tire which is 10 times harder to get off than the front.
Whatever their shortcomings, airless tires will prevent those scenarios.
