I can't tell from the picture, but does it have the proper spots to mount a rack? If so, one of those would be a nice, inexpensive upgrade.
Alternatively, how do your parents feel about you riding after dark? If they don't put a blanket ban on it, a nice headlight and some LED blinkies won't cost too much, and can move from bike to bike as long as they hold together.
Got a decent bell? They're like 5-10 bucks and help a lot in just about every possible circumstance.
A decent repair kit would come in handy, too. Spare tube and tire, some tools, a tire pump that fits on the frame...Shouldn't be too expensive, and if you're looking to go from "biking for fun" to "biking as main method of getting around town", the extra reliability will give you more actual security, and probably help smooth over any problems your parents might have with the possibility.
In general, I'd say stay away from direct upgrades to the bike. There's not much you can do that wouldn't be better spent just saving up for a nice new one. Useful accessories can always be transferred along, so they hold up a lot better.