Actually, the game is not that difficult to get into. First of all, you would like to play simple decks at the very beginning.
It is best to buy the following expansions:
Honor and Profit - great value for money,
Opening Moves - it has the most important Corp card ever released, Jackson Howard,
Double Time - has a very important code gate ICE - Quandary and an awesome agenda - NAPD Contract
All the cards up to C&C allow you to build a decent, straightforward Andromeda + Datasucker deck, which you can take to any tournament. If you buy Honor & Profit expansion, the addition of the cards like Security Testing and Legwork may even win you that tournament.
As for the Corp, the aforementioned expansions will allow you to make a decent HB Fast Advance style deck.
Both decks are easy to play and win a lot. With full cardpool you would be able to build slightly better variations of these archetypes, but you will do just fine with all the expansions I mentioned here + your current collection.
HB: Engineering the Future
3x Accelerated Beta Test (Core Set)
2x Gila Hands Arcology (Creation and Control)
3x NAPD Contract (Double Time)
3x Project Vitruvius (Cyber Exodus)
3x Adonis Campaign (Core Set)
2x Eve Campaign (Humanity’s Shadow)
3x Jackson Howard (Opening Moves) •••
2x SanSan City Grid (Core Set) ••••• •
3x Biotic Labor (Core Set)
3x Green Level Clearance (A Study in Static)
3x Hedge Fund (Core Set)
1x Archived Memories
3x Eli 1.0 (Future Proof)
3x Wall of Static (Core Set)
Code Gate (6)
1x Enigma (Core Set)
2x Inazuma (Honor and Profit) ••••
2x Quandary (Double Time)
1x Tollbooth(Core Set)••
2x Guard (Honor and Profit)
3x Ichi 1.0 (Core Set)
As for playing the game - familiarize yourself with main Corp archetypes and you will do just fine:
NBN: Near Earth Hub tries to win fast by scoring agendas in 1 turn thanks to Biotic Labor and SanSan City Grid. Be aggressive, run a lot! you are on a clock:
Jinteki Replicating Perfection - a lot of strong ICE, tricks allowing to score agendas during 2 turns (Caprice Nisei, Ash). Try to get points from R&D and H&Q, trash drip economy cards like Sundew and Mental Health Clinic whenever you can.
Weyland identities - have more money than your opponent. Always :). They will try to tag you after a succesful run and then deal you at least 4 dmg to flatline you.
Net Damage Shell play
Jinteki: Personal Evolution - be careful ,run with at least 4 cards in hand, preferrably with 5 or 6. They will try to kill you through Net Damage.
Runner archetypes are not so important to be familiar with to have a decent game. Just remember that Criminal's Account Siphon is always a threat, so are Noise's viri with his ability. Cards like Medium and Legwork can ruin your day. Jackson Howard is a lifesaver in all the match ups, always play 3 copies of this card.