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what test to use to avoid type-1 error?

I have some clarifications regarding using t-test. My study is a comparative study where I've collected data from two different countries. In order to compare the data, I am using t-test. However, using this test multiple times increases type error. An alternative can be ANOVA. But my concern is how can I use ANOVA to compare the demographic variables (age groups -3 categories) of two different countries? For example to find out how the younger group in country 1 is different from the younger group in country 2?
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It is true that multiple t-tests will increase the likelihood of error, however, there is a post hoc test called the Bonferoni test which supposedly corrects (somewhat) for this.  You might consider looking into this option.  Otherwise, you can still use a two-way ANOVA to do the multiple comparisons you are interested in.