The cheapest way is to send your money from your bank account directly to your bitcoin wallet created in bitkonan site or localbitcoins but I prefer bitkonan because they look faster for me with very low fees.In bitkonan you can also buy/sell crpytocurrencies to make a money but you can also save your earnings so that means that it can be your bitcoin wallet and there is not neccesary to have other bitcoin wallet ,only if some invesment site want from you to use some kind of bitcoin wallet then you must use more wallets and then 1 bitcoin wallet isnt enought.I dont know any other kind of deposit which we can make faster.Only I know that xapo offer a deposit with credit card but I dont know how much time it need to pass to get a deposit directly in own bitcoin wallet.
I often look at localbitcoins and their fees are much higher than kraken or gemini, I just looked at bitkonan and their fees are .29% which is more than krakens .2% taker fee.
Why are you not trying face to face meet up because in my view its better for saving fees just talk and give time to seller for meet up and other details then buy bitcoins because currently its best way to cut fees if you can do this safely