(almost) All the nouns ending with "a" are feminine - la silla, la mesa, la casa, la luna, la montaña. (Notable exception: el agua). Also feminine all that end in "ción" such as: la nación, la configuración, la confirmación.

Almost all the other nouns are masculine - el carro, el niño, el oso, el barrio, el avión, el camión, el árbol.

Pretty sure with those 2 simple rules you will catch 90% of genders right.

Actually, agua is feminine. But it takes el instead of la because it starts with an accented a. The common language-learning advice is "Don't learn the genders of nouns; learn the articles that go with them." But it doesn't quite work in Spanish.

poeta, nauta are two -a nouns that are masculine; sofa if you count a with accents

Nauta and poeta are both members of a small set of profession words which are masculine despite being in the first declension (-a) in Latin. My textbook provided a comprehensive (again, small) list and just suggested they should all be memorized; the only other one I remember now is agricola, farmer.

Manus, hand, is one of an even smaller set of feminine fourth declension nouns. I believe this oddity has also been preserved in Spanish as "la mano".

This makes me wonder whether the Spanish words for trees tend to be feminine while having masculine-looking forms; that is regular in Latin.

most nouns ending in -ma (but not all) are masculine. Basically the ones with Greek roots. I was taught -ma is masculine like your mom.