First of all, his post was written back during the dark days of TF2, before the class updates. His guide assumes you have the standard Shotgun, Pistol, Wrench combination.
However, which weapons you want depends entirely on what you want to do with them.
Use your Pistol versus enemies at a distance and the Shotgun for medium range. Wrench is, of course, for close combat. Especially for servers that have critical hits on.
Your wrench causes buildings to advance one build "step" when you hit them while they are deploying, except in the case of the Jag, in which case buildings advance two "steps" when you hit them. This applies to your allies buildings in addition to your own, and buildings that are being redeployed.
Personally, I play Engineer in one of these two modes:
Mobile Fortress Engineer
This is both an offensive and defensive build.
Typical loadout for this is Shotgun, Pistol or Wrangler (your choice), and The Jag.
The focus here is on building your buildings near the back lines, then picking them up and moving them forward. This can be used in combination with teleporters to bring buildings up quickly.
Hitting buildings with your Jag as they deploy or redeploy causes them to deploy faster than the standard wrench. Hence the emphasis on this build if you plan on moving buildings around.
Note: If you're on defense at the start of a round, don't build at your spawn and move it. Instead, build your teleporters first, then your dispenser, whacking it with your Jag to make it build faster. Once it's nearly up, go grab an ammo box and start building your sentry gun.
Note: On 5CP maps, consider building on the second point to start, in case the other team manages to cap the middle point. You can always move your gun forward if your team caps the middle.
Personally, I'm terrible with the Wrangler, as I tend to get sniped or backstabbed when I'm using it, but you may have better luck.
Since the Jag makes all buildings build faster than normal when you hit them, this is also a great build for assisting other Engineers.
Typical loadout for this is Frontier Justice, Pistol, and Gunslinger.
This is primarily an offensive build, but can be used to provide backup to normal Engineers on defense. I'll touch more on this below.
The Gunslinger's mini-sentries are surprisingly effective versus the 6 lower-hp classes (all but Demoman, Soldier, and Heavy). That you can build two of them (not at the same time!) with your 200 starting metal is a bonus.
Don't be afraid to destroy your mini-sentry to gain crits for your Frontier Justice, particularly since mini-sentries cannot be repaired. This is why you have the Frontier Justice in this build: Every kill or assist your sentry has when it's destroyed adds to the number of guaranteed crits your Frontier Justice gets.
Just be careful not to stockpile too many crits. If you die, they reset to 0. In fact, it's easier and safer to destroy your sentry and rebuild it elsewhere instead of trying to move it, as you don't gain the crits it had saved up if it dies in your arms, and you're unable to shoot whilst moving buildings.
When backing up normal engineers, if you coordinate you can build your dispenser for him and he can focus on getting his sentry up quicker, with your dispenser for resupply. This is especially helpful for rebuilding quickly after a big push wipes out your team's defenses.
Note: Your mini-sentry isn't that strong. Quite often, you'll need to "help" it by attacking enemies with your shotgun or pistol at the same time.