Remember: in informal Spanish in Spain, igual, a lo mejor, and lo mismo are by far the most common way of translating 'maybe'. Quizá, and to a lesser extent tal vez, tends to be used more at the end of the sentence or alone as a response; in written or formal Spanish, quizá(s) and tal vez are far more common. [See quizá+ subjuntivo/indicativo]
-Igual me quedo — Maybe I'll stay [Siempre seguido del modo indicativo]
-Igual no es el mejor momento — Maybe it's not the best time
→Quizá no sea el mejor momento [Más formal/culto; normalmente seguido del modo subjuntivo]
→→Puede que no sea el mejor momento — It might not be the best time [Otra alternativa; véase puede ser / puede que sea]
-A lo mejor hoy prefieres estudiar — Maybe you'd prefer to study today [Casi siempre seguido del modo indicativo]
-No me coge el teléfono -A lo mejor es porque no quiere hablar contigo — He won't pick up the phone -Maybe it's because he doesn't want to speak to you
-Lo mismo te llevarás una sorpresa — Maybe you'll get a surprise [Seguido del modo indicativo]
-Se está comportando de una forma extraña -Lo mismo te vio ayer — He's acting strangely -Maybe he saw you yesterday
-Iremos mañana, quizá — We'll go tomorrow, maybe [Después del verbo]
-¿Vendrás con nosotros? - Quizá /Tal vez — Will you come with us? - Maybe/ Perhaps [Como respuesta]