Latest posts for certain categories

I began making WP themes a while ago. I can create blog designs with basic WP theme layout including: header, content, sidebar, footer.

Now I wanna make something like news theme. I wanna display latest posts along with the recent ones for certain categories.
For example, If I have three categories named Sports, News, Tech… It would display the latest post of each category on the homepage.. and display the titles and date(not the whole post) of the other recent posts underneath the latest post..

I can make the design for it… but I don’t know how to code it in php..

Is there any template tag to display them or it should be achieved using some php codes?

Thank you