Normally, I tell people that the best bang for the upgrade buck is to upgrade tires. But there are no nice tires for a bike like that.

I would not buy handlebars or anything for that bike. You won't notice a performance improvement at all.

As cycleheimer says, this is a perfectly useful bike, so don't feel bad about it.

Oh, another favor to yourself: get a good pump, and keep the tires inflated well at all times. Learn how quickly your air escapes. You'll find it best to re-inflate every four to seven days. You can get away with overinflating the tires a bit, which will be a performance upgrade FOR FREE!

Here are some ideas, though. Buy one or two pairs of Kool-Stop brake shoes. That will help the braking, which is probably substandard.

Put toe clips and straps on, because these WILL give you a performance improvement, and they will make you stronger at the same time. You may have to change the pedals to do this, and that will be worthwhile. Your pedals have 1/2" threads, which are unique to (mostly) low-end bikes, so be careful when shopping. I have some pedals for you, and I will give them to you for the cost of shipping.

If you want to go really crazy, rebuild the wheels with alloy rims. They are $40 each. This will make the bike noticeably lighter, and it will brake better, too, because aluminum rims give better braking than steel rims do. But this is a mostly crazy idea. It could be fun, though.

Keep your chain clean and well lubricated.