Greetings commonenemy, and welcome to Call of Cthulhu! This is a fantastic game, and well worth the investment in my opinion.
Call of Cthulhu lets you run up to 3x copies of each card (by title), and most packs come with a playset (i.e. 3x copies) of each card, so you just need one of each asylum pack or deluxe set, with the following exceptions:
* Core set
- this comes with 1x copy of each card, so you'd want to buy three of these
* Secrets of Arkham deluxe expansion
- this originally came with 2x copies of each card, but has recently been reprinted with 3x copies so be sure to buy the 'Revised Edition' of this
* Summons of the Deep cycle
of six asylum packs (i.e. The Spawn of the Sleeper, The Horror Beneath the Surface, The Antediluvian Dreams, The Terror of the Tides, The Thing from the Shore, The Path to Y'ha-nthlei) - these originally came in 40-card packs with 3x copies of ten cards and 1x copies of another ten cards, but has since been reprinted in 60-card packs with 3x copies of all twenty cards so be sure to get the now-standard 60-card editions
* Dreamlands cycle
of six asylum packs (i.e. Twilight Horror, In Memory of Day, In the Dread of Night, Search for the Silver Key, Sleep of the Dead, Journey to Unknown Kadath) - this also came in 40-card packs, but is currently listed to be reprinted by FFG in Q3 2014
(undoubtedly in the standard 60-card version) so I'd hold off on buying these until that happens.