Yes, you need a new cassette! My husband just replaced the one on my new (used) mountain bike, but it does require special tools.

I would recommend taking your new (used) bike to a good LBS for a look-over and tuneup. They can replace anything needed and get it shifting well for you. Mine needed new shifter and brake cables, a new chain, and new pulleys for the rear derailleur as well as a new wheelset as the hubs were shot in the rear wheel. Replacing all this was a bit pricy, but I still got a good deal on the bike compared to buying brand new.

A good LBS can also fit you to the bike and determine if any fit-related changes are needed, such as a different length stem. You might need a different saddle to make your anatomy happy too, but you probably won't know about that until you ride the bike some.

If you don't have one already, make sure to purchase a helmet while you are at the bike shop!

Enjoy your new bike.

Emily