When we suggest a common plan, we say:
¿Quieres venir a casa? = ¿Te apetece venir a casa? – Do you want to come home?
¿Vienes conmigo / con nosotros al cine? – Want you come with me/ with us to the cinema?
¡Vamos a comer/cenar juntos! –
Let´s have a lunch / a supper together?
You can also invitar (invite) somebody:
¡Te invito a comer! – I invite you to lunch
¡Te invito a un café! – I invite you to have a coffee