tl;dr: I think the best route is to get NISEI’s System Gateway “complete bundle” which is available as print on demand or free PDFs for print & play. but read on for details, especially about the current state of card backs
SG has preconstructed “starter decks” designed to be a good way to learn or teach the game, but also has extra copies of cards to allow building decks using the normal deck building rules. This set is IMHO the best introductory NR experience, speaking as someone who has taught the game a lot over the past year. (btw NISEI recently commissioned a nice well crafted and short learn to play video)
After that, buying/printing System Update would make sense, this is a set of classic FFG cards reprinted with new art by NISEI, and together with SG make up a good “core set” and adds more variety in the deck building possibilities.
Beyond these 2 sets, buying/printing NISEI’s latest Midnight Sun cards before the previous NISEI cards (Ashes Downfall and Ashes Uprising) might make more sense as Ashes will rotate from the “startup” format in about 6 months (but still be legal in the larger standard format, which still includes some old FFG cards). Startup is a popular format and you may find people playing it at meet ups or cons, which is an advantage, but it’s also a great standalone card pool with a ton of variety and plenty of cool decks to netdeck from NRDB.
All of this needs to come with a caveat at the moment: SG, SU, and Ashes have different card backs than Midnight Sun, because NISEI removed the name from the card backs leaving just the stylized “N”. This caused a lot of drama on Reddit because you really need opaque card sleeves now, which was true mixing FFG cards but is now also true for NISEI only.
NISEI is going to release a remastered edition next year which will update everything to match, and have updated card text for core damage and other streamlined rules things. So it’s conceivable that printing and playing makes sense at the moment, if you want to eventually have all matching card backs.
Although I’m a fan of NISEI and think they’re doing great work, almost all Netrunner is basically pretty good. If you stumbled on an old core set and some packs or expansions from FFG days you’ll still have a great time. The old 2012 core set was not as great an on boarding experience, because the power level is all over the place, but it’s still pretty fun, I played a bunch with my old cards right before NISEI released SG and it was great.
However, do not pay extra for the FFG 2017 “revised core set”, it’s much more expensive on ebay only because there were fewer printed, not because it’s actually special. The 2012 core is more reasonably priced on ebay, but neither are as good a beginner set as NISEI’s System Gateway.
There’s a lot of FFG sets still in rotation in NISEI’s Standard format which is also popular as a format online and in person. These vary in price because again some sets at the end of FFG era had fewer printed. Some are absurdly priced. If you really want to get into Standard, it probably makes more sense to proxy specific cards in the decks you’re playing (always “legal” in NISEI events, and enabled by some tools made by the community, but obviously dubious legality in the eyes of copyright law) unless you happen to find an entire collection going cheap.
and although totally unnecessary, as you can play with lots of different physical bits to represent game state, you can find a variety of cool tokens made by various crafty people here, which may enhance your experience Near Earth Hub - Tokens