You will never, and I mean NEVER, produce sodium metal from electrolysis of an aqueous NaCl solution.  There is nothing you can do, no products you can use, no containment you can think of.  You will NEVER do it.  In the history of man, nobody has ever done it and nobody will ever do it.

The ONLY way to make sodium metal from table salt is to electrolyze molten NaCl.  Also, the theory that as soon as the sodium metal is produced it will react with the water is false.  Sodium metal is actually NEVER produced.  At the anode, you'll get the production of chlorine gas as the oxidation potential for the Cl- ion is about the same as that for the oxidation potential for water.  As a result, chlorine gas forms in a moderately concentrated solution of sodium chloride.  At the cathode, hydrogen gas is produced because the reduction potential of the conversion of water to hydrogen gas and hydroxide ions is -0.83 while that for converting Na+ to Na is -2.71.  The more positive the reduction potential is, the more favorable it is for the reaction to occur.

So at the cathode, the reaction of H2O + e- => 0.5H2 + OH- is MUCH more favorable than the reaction of Na+ + e- => Na (metal).  So what happens when you electrolyze a sodium chloride solution is you make chlorine gas at the anode and hydroxide ions at the cathode.  The sodium ions go unchanged, so the sodium hydroxide is the result of the formed OH- ions and the remaining Na+ ions.

Yes.  In fact, that's how sodium hydroxide is produced on an industrial scale.  They electrolyze a very concentrated sodium chloride solution producing chlorine gas and sodium hydroxide.  

The melting point of NaCl can be lowered a few hundred degrees centigrade by the proper addition of some calcium chloride.  Still, you need a fairly elevated temperature to make the mixture molten.  You will also need electrodes which are completely inert to the high temperatures used and the corrosive chlorine gas that is produced.  Another very important thing that's needed is an inert atmosphere over your electrolysis chamber.  Because of the high temperatures, the sodium that's produced will be in a liquid form.  Sodium is reactive enough as a solid, but at a high temperature in the form of a liquid it can actually be explosive.

Another compound that can be electrolyzed which has a lower melting point is sodium hydroxide.  The problem there is that anhydrous NaOH quickly absorbs water from the air so it's very difficult to keep the whole thing dry.  Also, molten NaOH is an INCREDIBLY caustic mess that can dissolve many supposedly 'inert' materials.  In addition, if some sodium forms in that molten mess and reacts with the tiniest bit of water, you'll get a little explosion which will fling molten sodium hydroxide all over the place.  That's a VERY dangerous thing.

If you truly want to learn more about the formation of sodium metal, go onto google and do a search for the 'Down's Cell'.  That should give you plenty of information about the electrolysis of NaCl.  

Yeah, NaOH is a real pain in the arse in terms of keeping it pure.  You can buy it in an anhydrous form of powder/flakes, but as soon as you open the bottle it will start to absorb water from the air.  KOH is really good at doing this, and when you open a bottle of KOH on a humid day, you'll immediately see it start absorbing the water.  Also, NaOH will readily absorb carbon dioxide from the air and form NaHCO3 on you.  So whenever you have powdered NaOH around, you need to keep the bottle closed.  For most purposes (Such as making soap or unclogging a drain), the sodium hydroxide remains pure enough for the intended purposes.

You would need a higher temperature to continue the electrolysis so that there would only be sodium left. Also that continued electrolysis should be done in an inert atmosphere

At this stage, you will be left with solid sodium hydroxide because all the water has either been electrolysed or evaporated due to heating effect. How do you intend to electrolyse a solid compound? The only way to obtain sodium is via electrolysis of a molten sodium compound.

I don't recommend it at all, if you carrying out the electrolysis in a home make-shift lab. you need protective equipment. let me quote some information from sodium MSDS:

Emergency Overview
--------------------------
DANGER! FLAMMABLE SOLID. CORROSIVE. WATER REACTIVE. CATCHES FIRE IF EXPOSED TO AIR. HARMFUL OR FATAL IF SWALLOWED. HARMFUL IF INHALED OR ABSORBED THROUGH SKIN. CONTACT MAY CAUSE BURNS TO ALL BODY TISSUE.

Health Rating: 3 - Severe (Life)
Flammability Rating: 3 - Severe (Flammable)
Reactivity Rating: 3 - Severe (Water Reactive)
Contact Rating: 4 - Extreme (Corrosive)
Lab Protective Equip: GOGGLES & SHIELD; LAB COAT & APRON; VENT HOOD; PROPER GLOVES; CLASS D EXTINGUISHER
Storage Color Code: Red Stripe (Store Separately)


Potential Health Effects
----------------------------------

Inhalation:
Inhalation produces damaging effects on the mucous membranes and upper respiratory tract. Symptoms may include irritation of the nose and throat, and labored breathing. May cause lung edema, a medical emergency.

Ingestion:
Extremely dangerous, corrosive material. Will react immediately with saliva to cause serious burns and possible local combustion and even explosion of hydrogen in the mouth or esophagus. The metal's low melting point can cause further complications.

Skin Contact:
Corrosive, can cause serious burns due to almost immediate reaction with water, especially on moist skin. If metal ignites, very deep burns and tissue destruction can occur.

Eye Contact:
Corrosive. May cause redness, pain, blurred vision, and damage from severe alkali burns.

Chronic Exposure:
Continued or repeated skin contact may cause dermatitis, mucous membrane irritation, and lung damage..

I had no intention to suggest sodium hydroxide heating should be done.
It appeared to me that many of the answers to this thread were incomplete or piecemeal.
So I put all the answers in one post and asked if I got it correct.
Obviously I was mistaken.

From your explanation ===
In item 2 if you stay at room temperature will you not get hydrogen and oxygen?
Also eventually will you not get solid sodium hydroxide because you electrolysis the remaining water leaving just the solid.
Item 3 then ensues which we are not recommending.

My point is that we can get rid of the water without heating – just continue the electrolysis.

Is this correct?