In each state it is different. I live in Texas and am very knowledgeable about the laws here, but I do know that Maryland (assuming that is where you live) is a "May Issue" state. That means you need to not only qualify, but also write a letter stating why you want the gun and the state "May Issue" the license. Here are some sites that will give you the info you are looking for:
http://www.usacarry.com/maryland_con...formation.html
http://www.ehow.com/how_2064603_get-...ed-weapon.html
The best I can tell, Maryland does not recognize any other states permits, so getting a Utah, Florida or Pennsylvania permit will not help you there.
You asked about carrying a gun in your car. It is illegal to have any loaded weapon in Maryland in your vehicle unless you get your CCW. Some states allow you to have one in the car, but Maryland is not one of them.
If you are able to get a permit, you also need to be very careful when you travel. Washington, DC DOES NOT allow you to have a weapon and will not recognize your permit. So you would have to leave the gun home whenever you travel there.