It depends on your jurisdiction, as that will affect which credit cards (if any) are accepted. For me, it costs 4% to buy via credit card, which I think is crazy, but for some people it's totally acceptable.
In my locality, high volume cash sellers (the few that still exist) are charging 2-6%. But I generally wait for someone to take my offer at 0-2% profit. I also have some old contacts who often need liquidity and will pay spot price so they can keep charging a mark-up to the newbies.
If you are in the US, I would ACH transfer to Coinbase (free) and transfer to GDAX and buy via limit order (free). If in Europe, I'd probably go with Bitstamp and use SEPA. You might consider putting up your own offers on LocalBitcoins, too.
Also correct, in fact the rates I just mentioned are from online traders (who would then have to complete trades via escrow). They have much, much higher rates for other offline methods (cash deposits, face-to-face) but I prefer to stay away as I don't really want to take the risk of getting robbed or scammed - not that all of them there are scammers!
There are also others I know of - high volume cash sellers like you mention - who operate via Telegram/IM but with these, you again have to trust that things will happen quickly and they always require you pay first.
And, yes, if you want to buy big volume, put up your own trade at the rate you like. There's bound to be offers.