The bike should work.

You can do a half an hour ride on just about anything. Once you start getting up to an hour or so rides, then you might start looking at a road bike or drop bar cyclocross bike.

I assume you're having troubles with the front derailleur on your existing bike. Grip shifters? New (or used) shifters are cheap. Try to find a bike co-op that will give you some instruction on bike maintenance, or perhaps take a class on bike maintenance. It will be well worth it in the long run.

Even a new bike will need some maintenance, and derailleur adjustments.