Saving File Space with Drupal 8
While you could uninstall and delete core modules, I wouldn't recommend it.  They will be restored during updates and you'll have to constantly be vigilant to not go over your space limit.

Over time, the size of the site will probably grow slightly due to additional updates, and you may add files of your own (images, etc.) that also increase the site's size.

Drupal 8 requires significantly more space than Drupal 7 and is a very tight squeeze if you only have 250 MB.  Hosting recommendations are off topic for this site, but there are many hosts that offer more file space (say, 1 GB) at a reasonable rate.  If Drupal 8 otherwise fits your needs, I would pay more to increase the disk space, but if that's not an option, go with Drupal 7 since it's smaller, even with a fair number of contrib modules.