Based on experience, banks here in the Philippines tend to be really crypto-friendly; at least as of now. Though personally I'd pick either BDO, Metrobank, or BPI. In terms of cost efficient probably Metrobank, but their online banking sucks in my opinion. Personally, I'd go with BPI. Not sure about the most cost efficient though.
As for crypto-fiat exchanges, most would suggest Coins.ph[1] as it's a lot more famous here, but I'd personally go with Abra[2]. The price premiums are significantly lower with Abra than what you'd get with Coins.ph. Having a Coins.ph account is also good though, as you can use it to buy mobile load in exchange for bitcoin. Basically, Abra for crypto<->fiat, and Coins.ph for mobile load and bills payments and such.
Feel free to ask more questions, and I hope you enjoy your stay!
-- Data --
Coinmarketcap(CMC) price: ₱593,224
Coins.ph buy price: ₱605,388
Abra buy price: ₱601,365
Pricepoint: August 11, 2019 | 01:30 AM GMT+8 (Philippine time)
within a few seconds apart between platforms(possibly with small price fluctuations)
-- Buy Price Differences per 1 BTC --| Data Sources | | | Price Difference | | | Percentage Difference | |
| CMC vs Coins.ph | | | ₱12,164 | | | 2.02% | |
| CMC vs Abra | | | ₱8,141 | | | 1.36% | |
| Coins.ph vs Abra | | | ₱4,023 | | | 0.67% | |
[1]
https://coins.ph/[2]
https://abra.com/