SCHB is a fine choice for the US stock market, with ~2500 stocks that cost 0.03% in expense ratio.
Last year Vanguard introduced $0/trade for all ETFs, both Vanguard and non-Vanguard. In order to stay competitive, Schwab and Fidelity followed suit. That means at Schwab, you can buy any ETF - not just Schwab ETFs - for $0/trade. So for your international allocation, I'd favor Vanguard's ETF over Schwab's - and it will cost the same to buy/sell.
Vanguard Total International (VXUS) holds ~7400 stocks with an expense ratio of 0.08%. It tracks the "FTSE Global All Cap ex US Index", meaning both developed and emerging markets. It's top holding is China's tech giant "Alibaba".
Schwab International ETF (SCHF) gets a lower expense ratio (0.06%) by holding only ~1500 stocks, and avoiding emerging markets. Per the fund's description, it tracks the "FTSE Developed ex US Index", and doesn't hold "Alibaba" at all.
Emerging markets are important - that's why China is 8% of VXUS. If you only buy SCHF, you will allocate 0% to China, so for international, consider VXUS. At Schwab you will pay $0 to buy and $0 to sell non-Schwab ETFs, and can get better diversification by doing so.