The "Republish" required only when bringing a new web database online or creating a new publishing target etc. Copied the below highlighted paragraph from Sitecore document,
Republishing removes all obsolete versions from the target database.
You can use republishing to bring a new web database online, to
restore a backup of the master database, and to add a new content
language, a new publishing target, or other system items to the
I guess in your case, you are not creating a new web database/publishing target, you are planning to use the web DB which comes with the Sitecore installation. So technically "Smart Publish" should be efficient.
I Just ran the Smart and Republish in two plain Sitecore 8.2 local instances separately, the time taken to complete the publish might vary due to various external parameters as well, so ignore the timing in the below logs. But the Republish is always overwriting/updating around 4625 items in a plain instance which might be an additional overhead, because those are already available in the web db.
**Sample Smart Publish logs from plain instance**
21148 14:18:00 INFO Finished [Publishing] - ProcessQueue in 5773 ms
21148 14:18:00 INFO Publish Mode : Smart
21148 14:18:00 INFO Created : 0
21148 14:18:00 INFO Updated : 0
21148 14:18:00 INFO Deleted : 0
21148 14:18:00 INFO Skipped : 4627
**Sample Republish logs from plain instance**
18628 14:25:59 INFO Finished [Publishing] - ProcessQueue in 260689 ms
18628 14:25:59 INFO Publish Mode : Full
18628 14:25:59 INFO Created : 0
18628 14:25:59 INFO Updated : 4625
18628 14:25:59 INFO Deleted : 0
18628 14:25:59 INFO Skipped : 2
Note - Whatever changes you make on top of the instance, only that needs to be migrated/published to the web db and "Smart Publish" can do that.