Use the same passport to enter and leave a country.

I use one of my passports to enter and leave the country in which I’m resident, since the stamps build up and I don't want to have to renew this one any earlier than I have to. I use the others for other countries.

To enter (and leave) any given country choose the passport based on whether it will avoid having to get a visa (since you are talking about two passports from the same country this is irrelevant).

I’ve changed passports (different countries) many times in this way to simplify entry - when arriving by air I’ve never had any questions; on land borders I have only once been questioned (entering Paraguay) on why the passport didn't have an exit stamp from the previous country (Argentina) - I went back and asked for an exit stamp in the relevant passport and the Argentine Immigration Office had no problem in giving me one.

Always stay within the permitted periods in each country.

I've never found a country which doesn't permit more than one passport for foreigners - many countries don;t permit more than one passport from citizens, but passport rules are for the issuing country, no business of the country you're visiting - if the USA or UK (to name countries which I know permit more than one passport) permit this it's their business.