Cool idea Greg.
I actually tend to pad out overseas orders with extra Moras and Opinels if the vendor has them, so I always have some 'stock on hand' to introduce friends to decent quality knives. I sharpen them up and strop them before giving them one of each. They're usually over the moon when I check back with them, generally commenting that the cutting performance is better than any knives they've ever used.
For my $100 starter set, I'd choose a Opinel No. 8, an Ahti Korpi puukko, and a GEC Tidioute 14 in ebony.

The Opinel No. 7 was the first traditional knife I used for EDC and it's what I learnt to sharpen on. Its thin blade is easy to get good results with. After giving away a bunch of Opies, I tend to only give the 12C27 stainless blades now. Most people don't really respect knives like we do and can be daunted by 'tarnish' and corrosion damage resulting from what we'd regard as sloppy maintenance or misuse. I'd rather give a working knife first up that they can learn to maintain, sharpen and use and not worry too much about 'wrecking'. Like many good things, appreciation of a carbon or tool steel blade is learned, and comes with time. I saw a thread on here only a few days ago where a young feller announced he'd 'ruined' his knife because it was blunt!

Ok next knife. The Ahti knives from Kauhava in Finland are tremendous value for money, and there needs to be a good fixed blade in the set. Again, Scandi grinds are easy to learn to sharpen on and stout enough to do tasks you wouldn't attempt with a folder. They use a similar lightly alloyed carbon steel to Cases CV but run quite a bit harder, and you can't go wrong with a puukko.

Lastly, the 'down the rabbit hole' knife - this could be any of a number of GEC models - I chose the 14 Boys knife in ebony because it's available and the price just snuck the total cost in at under $100. This is a 'Sunday' knife, and serves as a taster of what a pleasure a really nice knife can be as you go about your daily life. The size of this knife is why I specified an Opie No. 8 earlier and not a No. 7. Ebony covers - because it's tough, durable, warm to the hand and attractive to the eye. I've refurbished old knives for friends where the ebony almost looked new, while the brass and steel bore all the scars of a lifetime of heavy use.
Basically this is a knife to appreciate after the workaday basics have been learnt with the Opinel. It's a knife for finesse use that will make the user feel good each time they take it out of their pocket to use or admire it.
I often have people who use junk or throwaway knives assure me they don't need a $(insert price here) knife, when I recommend something. I've found the best response to this is to just get one into their hands whether as a gift, loaner, trade or sale, and you can see that new appreciation growing, the next time you show them a good knife, rather than just asking how much it cost.
Well it's certainly been instructive to read everyones choices. Some of you really got some serious mileage out of that C-note! But these are my recommendations for use around these parts.