My son just bought a very old (1916 manuf date) with matching serial numbers  Lee Enfield.  However, it does have some rust in the barrel and some of the outer surface.  Please let me know what would be the best way to remove the rust without applying a lot of chemicals.  Your help would be greatly appreciated.

Good for your son they are stupid fun rifles.

Look up the "penny" method maybe? I've seen it but don't know how legit it is.
I would start with maybe 0000 steel wool, lightly, with oil.

But real rust removal experts will tell you better than me.
Enjoy that rifle!

ETA: just saw the "inside the barrel", again, others will come along with better advise than me. I've used the penny on outside surfaces with very light rust to good effect.

Do you have access to a bore scope?

Start with a regular cleaning, don't use anything harsh. It will arrest the trivial rust, and remove any gunk so you can examine the condition without doing any harm.

Some bbls are so pitted that they shouldn't be shot.

What you see determines a course of action. For example, if there is very deep pitting you will need professional advice. If the rust is very superficial, you may be able to use JB Bore Paste on felt pellets to clear it up.

External rust is always a debate on these collectible surplus rifles. Some would say to scrub it off, others would argue to leave it but arrest it with a mild cleaning and then leave it with a coat of oil.

I would tackle the bore if he plans to shoot it at all, and see if it looks deep or badly pitted.

The "penny" method is basically using copper to scrub off the rust without damaging the finish. Since pennies are now copper-plated zinc, it may not work as well. Other proven methods are Kroil or light oil, plus brass wool (Brownells has it), 0000 steel wool, or simply a hunk of wood. Speaking of wood, if the stock is as bad as the metal, Kramer's Furniture Restorer works excellently. I used it on Martini-Henrys from the Nepal cache.  
As to the bore, there's likely a lot of fouling along with the rust. Remove the wood, and use one of the foaming bore cleaners (Wipe-Out, etc.). It will probably take numerous applications, alternating between patching and brushing. Some milsurps have taken a month or more to finally come as clean as they are going to. Once the fouling is out, Evaporust will take care of any remaining bore rust. It also removes bluing, so use caution.
Electrolysis is certainly faster, but somewhat fiddly, and I've never gotten good results. Others have excellent results, so it's probably operator error.

Put a rubber stopper in the barrel and put some hoppes 9 in for a few hours, then pour it out. Get yourself a chore boy scrubbing pad and pull out a clump of its scrubbing metal shavings and thread them onto the end of cleaning rod, and use this to scrub the rust out. You might need to repeat the process a few times. You might also try sweets 762 in between the repeat of the process. One other process I sometimes use if it looks like a sewer is reverse electrolysis, you can make a simple bore cleaner using a lantern battery and five bucks of hardware from Home Depot. There’s a lot of diy plans on the net.

You should also consider that after you do all this,it may still look bad. I had this happen with a matching k98 I found in a barn, it was really bad, thought it was never gonna be a good shooter. After all the steps above, I just took it out shooting as I was about to give up on it. After shooting, the stuff in the barrel loosened up and it turned out to be a decent barrel. The heat and pressure from firing made a great difference!

Bronze, brass, or nylon brush with some 3in1 oil on it. If you use brass, you will have to rub the brass marks off after.
Steel wool is how you strip a finish not remove rust.
Or you can always take a wire wheel to it...