Whats the best way to save a new entry in my plugin?
You can use the FrontEnd Entry Form for this. If you want to allow guests (non-registered users) to submit the form, you need to use the Guest Entries plugin.

Both methods will set "publishing date, id, etc" automatically, you just need to specify the title in the form.

If you want to hard-code some field values and prevent the user from changing it, you'd need to create a plugin which checks for entries.onBeforeSaveEntry or guestEntries.beforeSave (if you use Guest Entries plugin).

Edit:

The Entry Form is just an example. You can just as well use an ajax-request to send your data. Just make sure the POST values are set correctly.

If you want to save an entry from within your plugin, use the EntriesService API