You can absolutely acheive this with WordPress, and I’d add that WordPress is specifically designed for these exact needs (posts, archives, excerpts, etc.).
Using the default functionality, you can easily choose how many posts to display on the home page (or main posts page). You can also use the “more” feature to define post cut-off points where the “read-more” link will go. etc.
Of course, you can customize it further by tweaking your theme or using a pre-made theme. The codex is also very helpful.