As somebody who is among the few to complete several early sets, when you get to collecting for the pre-NES systems, you start to realize that sometimes no amount of money will suffice for buying certain titles, and that time and pure luck are required. You can't hope to buy something that simply can't be found for sale at any price. Also, the size of a system library has nothing to do with how easy and quickly it will be to get every game in it, given how infrequently some titles ever come up for sale.
Magnavox Odyssey: Percepts, as it was a mail away and distributor bonus game that few got. The second wave of 4 games from 1973 are a close second contender. The odds of finding any of these in the wild after nearly half a Century are very slim. Ebay or a fellow collector are your only chances here. Only around 27 games in this set.
Fairchild Channel F: Most will say that #19: Checkers is it, but the real brutal one is the Democart, which was sold via mail order and even given a box. A few Democart 2s exist, but were never sold publicly. 27 games in the US retail set, and good luck.
RCA Studio II: None, really. This is actually the easiest US system to get a full retail set for, even boxed. There's only 10 games to get. The Bingo game is actually just a sales sample that was never sold. The two rarest retail games, Gunfighter/Moonship Battle and Speedway/Tag, turn up several times a year and go for at most around $100-$150 in good shape. Biorhythm goes for just slightly more than a copy would have cost back in the day when adjusted for inflation, and the other 7 can all be had complete for their original retail prices, which given 40 years of inflation means they've actually gotten cheaper over time. This system might also have the highest percentage of games still CIB, if only because they were rarely played back in the day. A complete collection of all games and a boxed system can be had for under $400 shipped.
Magnavox Odyssey 2: Power Lords, though it is "only" a few hundred for a complete copy. Only 49 games in this set.
Astrocade: Possibly the second easiest US system to get a full set for, if you only consider that most of the "third party" releases weren't necessarily licensed. There's still plenty of NOS for the actual main releases. Good luck getting a working system to play them on, though. 26 games in this set.
Vectrex: As said above, Minestorm II, and possibly Mr. Boston. The backstory of Mr. Boston just isn't well known enough to consider it a retail release. 28 games in this set.
Telstar Arcade: As said above, good luck finding Cartridge #4. Loose ones turn up fairly often, but complete copies are rare- far more so than any NES game. Only 3 extra games for this system, but you'll have an easier time completing collections for systems with much more extensive libraries. This was both a retail and mail-order release.
Emerson Arcadia 2001: #12: Red Clash, followed closely by #24: Spiders, and until recently #21: Grand Slam Tennis. Internationally, the Italian exclusive 3D Attack. Don't even bother with this set, as you will never see these games in the wild, and they can go years between Ebay appearances in any condition. To put the challenge into perspective, there are more copies known of Air Raid for the 2600 and more copies of the NES competition carts known than there are of Arcadia 2001 Red Clash. And no, foreign clone versions don't count- you can't substitute the Leisurevision versions and still consider it a complete set. If a few of the surviving copies hadn't been purchased directly from their original owners who happened to get them at retail back in the day, there would be serious grounds for doubting that these had ever even had retail releases. 22 games in the US Arcadia 2001 set.
Atari 2600: The one system that nobody is known to have a complete set for, or even a copy of every game.
Collector's Quest Podcast 
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