I can give you a list of the main archtype Core books for both 4E and 5E
5th - Chrome Flesh (Augmentations and Drugs), Street Grimoire (Magic Book), Data Trails (Matrix Book), Run & Gun (Equipment and martial arts book), Run Faster (Quality and lifestyle book similar to 3rd's Shadowrun Companion), and Rigger 5.0 (for Riggers obviously), though a recent edition to these is Cutting Aces (a Face Core book) also Howling Shadows (Critter Book)
4th - Augmentation (all the Cyber and Bio), Arsenal (Guns, explosives, and Vehicles), Street Magic ( Magic...), Unwired (Matrix stuff, kinda complex IMO), and Runner Companion (Metavarients, Qualities and such) Also Running Wild (Critter Book)
Alot of these rulesets are similar in play with some specific differences between editions kinda like D&D 3.0 and 3.5. Seeing that 4th ed is already completely done, you might be able to pick up these books at used book stores on the cheap. 5th is the current edition so is supported by things like missions play and alot of online games, but as far as which one you should get I can't answer as I have the core books for 2nd through 5th ed. No matter how many editions they make I'm gonna buy them. I'm a lifer. Hope this helps.