With the first option (default) "Start a new recovery point set the first time the backup is run in a new month". It would have created a base recovery point at the start of every month. e.g., if you set "Limit the number of recovery point set save for this backup to "3" as default it would have 3 base backups for every 3 months and on the 4th month after doing the base backup it would delete the oldest recovery point. So at any given point in time you would have 3 recovery point base backup and rest would be the incremental backup. If we consider there are 4 weeks in a month and you do backups from Monday - Friday. You would have 1 FULL (v2i) file and 19 Incmental (iv2i) files.
With the above example, after the 2nd base backup is done on the start of the month all the previous incremental backups (iv2i) files would be deleted and would have only the base (v2i) recovery point. Same goes fro the 3rd base backup on the start of the 3rd month.
For the Second option "Start a new recovery point set the first time the backup is run in a new week" same thing would happen considering the above example. Only difference would be that it would happen every week instead of every month. So you have base recovery point (v2i) created every week instead of every month. So if you take backups from Monday - Friday, you would have 1 FULL (v2i) file and 4 Incmental (iv2i) files.
Second option is a better one if you need frequent FULL backups. Also restoring the data is faster since there wont be too many incremental backups as compared to the first situation.
Hope this helps to answere your query.