There are many common misconceptions when it comes to radios. Everyone has their own opinion on what someone should start with in the RF world. Let's just say all those posted above me have pointed out everything I would also. But maybe, just maybe it hasn't been mentioned, how your coax has been run. If it's in a tight bend or pinch, there's a chance the center conductor has migrated and is causing a short in your antenna system. You definitely need to check your SWRs or have them checked by someone that knows what they're doing.
You will want to step away from "bargain" type antennas and get something decent, I'm not saying go get the best competition style you can, anything other than those cheap fiberglass whips sold in truckstops is an improvement. However, Wilson Silverload antennas are good, a general rule of thumb I like to follow is, I never buy a fiberglass antenna shorter than 4' long.
You say you have a Cobra 29, as does your buddy. You both have built in SWR meters on the radios to help get you in the general range of where you should be. I honestly don't put much faith in those meters, but it WILL read close to what your readings are. It will put you in the safe range anyway. You'll want to make sure all parts of the antenna stud are put together properly, that your coax is in good shape, and that you have a good ground for your antenna bracket/mounting location.
I agree that a mag mount would be good but as you already have something to work with, I say go with it. If you were to buy a mag, I'd recommend a Wilson 500, 1000, or 5000. They're all great for what they are. Best of luck to you, let us know how it works out.