Moving to New Server, What Did I Do Wrong?

I’ve been helping (or at least trying to!) a friend move the site for the family business to a new hosting company. The site is gbrusso.com and the “new” location is https://50.87.249.162/~gbrussoc/ if the regular URL doesn’t work. We finally got Network Solutions to release the domain name and we transferred it over to the hosting company so that the domain and hosting are in the same place. I thought I was going about this “site copy” the right way, but I think somewhere along the line I must have messed up because the site isn’t working the way it should. Many of the links go to 50.87.249.162/~gbrussoc/pagename instead of gbrusso.com/pagename and I can’t log in to the Dashboard unless I go to https://50.87.249.162/~gbrussoc/wp-admin. Here’s what I did when I was moving/copying the site, and hopefully you guys can tell me where I went wrong and how to fix it.

I copied the database and the files from the old site location.
I had them sign up for hosting with the new hosting company.
I installed WordPress in the new location.
I used WordPress’s own import plugin to import stuff from the old site.
Some parts of the site didn’t make the trip, so I recreated those.

Now gbrusso.com is pointing to the new location, but if you poke around on the site you will see that some aspects are not working properly. Hopefully I didn’t screw up royally! ??

(FWIW, the new hosting company is BlueHost and their servers run Linux.)