I am not familiar with WV law, so I can't comment on reciprocity specifically. Try handgunlaw.us or usacarry.com.
However, I travel by air frequently, and yes, you can take your gun in checked baggage with most airlines. The exact procedure depends on the airline. I would recommend that you take a look at the carrier's web site and look for a section on baggage. Firearms are usually listed under "sporting goods." Additionally, look at the TSA web site for TSA requirements. Note that many airlines' requirements are considerably more restrictive than the TSA.
The basic run down is this:
1. The firearm must be unloaded (duh...)
2. The firearm must be in a locked case.
3. Ammunition must be in an enclosed carton designed for holding ammunition, such as a cartridge box. Loaded mags are usually NOT ok, unless you have a cap that covers the top of the magazine. That said, many TSA screeners and airline reps interpret the rule as no loaded magazines.
4. The firearm must be declared to the airline, and an affirmation that it is unloaded (signed red tag provided by the airline) must be included in the case. Note that the tag frequently looks like a luggage tag--it does NOT go on the outside of the bag, no matter what the airline rep says. Ask for a supervisor if you are told to put the tag on the outside of the bag. Be aware that some airline staff don't know procedures for this, and there is also a form for law enforcement to carry on the aircraft while in performance of duty. This is not the form for you. I have been erroneously presented this form several times.
Here is what I recommend for a handgun:
1. Get a hard-sided handgun case and a chamber flag. Unload the firearm. Install the chamber flag in the gun and put your gun and empty magazine in the case and lock it with a NON-TSA key lock. Don't put the ammo in the gun case.
2. Put the case with the gun in your suitcase. Put the ammo (inside the cartridge box) in the suitcase, unless the airline requires that it be in a separate piece of luggage--I know AirTran requires this, but Delta and Southwest do not. Lock the suitcase with a TSA-lock. These can be opened with TSA "master keys."
3. BE SURE TO BRING THE KEYS ON YOUR PERSON! Go to the ticket counter, inform the agent that "I am declaring an unloaded firearm in my checked baggage." The agent will have you to open the gun case and show it to him/her and will provide you with the red tag to sign and put INSIDE the case. The agent should not handle the gun. A few airports I have flown through required a police deputy to inspect the firearm to ensure that it is unloaded. This is unusual, but they have always been courteous. Lock the case/suitcase and be on your way.
If you put a non-TSA lock on the suitcase, the TSA WILL cut it off. They will not cut the lock on the hard-sided gun case--cutting this is actually against the law. Be prepared to unlock the gun case again for the TSA after the airline has already inspected it. They don't usually ask, but they might--and sometimes this takes considerable time.
GIVE YOURSELF EXTRA TIME BEFORE YOUR FLIGHT. Most airline staff and TSA are knowledgeable regarding the policies, but some are not and you may need the extra time to deal with supervisors. Bring printouts of the TSA and airline policies with you. If any airline or TSA employee asks you to do something not in accordance with TSA regulations or airline policy, politely but firmly ask for a supervisor.
