ps. do you think I should delete the old blog once the transfer is made?
NO! NO! NO!
Get the site redirect to send all traffic from your old site to you new site - then people will not get lost - it will also send search engine traffic to your new site - ( if you are not moving content then just leave a note on old blog that you have moved to a new place)
Change the Perma Link structure on your new site to match your old site (get help at WordPress.ORG) - I am assuming that you have transferred your content to your new site -
If you are just starting a new Blog and not transferring the content - you can just leave a note on your old site that you have moved and give a link to your new site -