The price you pay for excluding all your earned income using the FEIE is being unable to contribute to an IRA (Roth or Traditional). The question of where to put your money seems pretty straightforward. Without a 401k option, it looks like you'll be using a taxable account for your investments.
The question of what to buy in that taxable account doesn't have a simple answer. As you probably know already, unearned income can't be excluded using the FEIE, so you'll be paying US taxes on capital gains/dividends each year you realize/receive them. It looks like you're safely in the 15% tax bracket now, so you'll enjoy the 0% tax rate for long term capital gains.
One possible approach: choose investments that minimize short term capital gains/dividends, and thus ongoing US taxes. Some mutual funds are "tax managed" for exactly this purpose, and you can check the last year's distributions to get an idea what to expect from any mutual fund/ETF. There's also BRK that never pays dividends, and it behaves more like a fund than an individual stock. This approach lets you decide when to sell in the future and realize a capital gain, which is presumably a long term gain by then. If the 0% long term capital gains tax rate remains for the 15% tax bracket when you do sell (and you stay within that bracket, of course), you wouldn't owe any US tax on that sale.
Just remember that minimizing taxes is only one factor to consider, so don't forget risk tolerance, time horizon, diversification, etc!
