I've done other LCGs. Would this be better with 2 core sets?

It depends entirely on how many players you plan to be.

1-2 players = 1 Core + expansions is sufficient

3+ players = 2x Cores are likely needed to build suitably strong decks

If you want optimized decks:

1-2 players -> 2 core sets

3+ players -> 4 core sets

The reasons for the above judgements are as follows. You can only have two copies per card(by title) in your deck. While every expansion has two copies(a full playset) of each new player card, the core set has only one copy of each card.

Like Star wars Lcg I personally liked this game more with more cores, because then you can include two of those cards that you really like in the deck... if you want to have two good cards in two different deck... then four cores is way to go... it all depends.

I assume with more than 1 core set, when you make the mythos deck and the bag, you only use those cards from 1 core set? The reason I thinking of more than one core is for the investigator decks.

Spot on, each scenario only requires you own one copy. 2 copies lets you keep all scenarios built and ready, but 1 core is certainly fine. The only benefit is maximising options for player deck building, hence the suggestions above for minimum and optimal versions.

Yeah I strongly advise planning on 2 cores if you want to play this game. 2 core boxes alone can support 2 players very well. With the expansion sets that expand the card pool and investigator choice I would say you can play 3-4 people if you own 2x core + current expansions pretty well.

Nice-looking table.

I struggled playing solo with just 1 core. A second core set allowed me to create much stronger and more reliable decks, so if you plan to play solo the second set is a must have IMO. Also, the second set means you can better accommodate more players.

I am currently playing one campaign solo, and another campaign with two other players. So I have 4 different decks (all different classes) and not had any issues (although I prioritise my solo deck as more players makes the game a little easier, whereas in solo mode I need a stronger deck).

I am playing with my brother ( 2 players always) and I am fine with one set. The expansions slowly bring better cards. And that is enough for me.

I have 2 core sets, a bag for the chaos tokens, and 1 each of the scenario packs on the way. I can't find Dunwich anyplace for sale.