Now if I select the 'erase disk and install Ubuntu' option, would those partitions be automatically created?
No. For starters: Ubuntu will no longer create a /swap. We use a swapfile nowadays. The default will use / and only /.
If you want full control over the partitioning choose "something else".
A regular desktop can do with a partition of 20 Gb for / and 5 Gb for /home and a personal data partition (remainder of the disk or a 2nd disk) with its own partition/mount point if you move the directories in there afterwards (so you basically use /home only for storing settings created by the system and not for your own stuff).
If that is not to you liking you can forgo that and set /home as large as you want.
The 20Gb for / is enough; you will never be able to install software from the repositories to the size of 20Gb. You will only reach that if you store personal data in / (like a website, mysql database or videos or something similar) and those should be on a different partition anyways.