I would simply add a field to your Users table is_admin and make it boolean, if you're only ever going to have two types. Having a User method IsAdmin() would be the only thing you'll ever need.
But if you want one level up from that, you can create roles and role_user tables, with the latter being the pivot for roles and users. I'm assuming that you know how to create and implement your own middleware. If not, I find the Laravel docs outstanding and use them daily. All you need to do then is create a route middleware class DoSomething and Gate::definition to make sure the $auth()->user()-can('do-something'); So a Gate definition in the AuthServiceProvider, DoSomething middleware class, route file reference ->middleware('do.something'), and register the DoSomething::class in the kernel.php.
I'm currently looking at diving into the spatie package myself because it looks way more robust, but there's definitely going to be a bit of a learning curve to implement it. But look at its usage, you can't beat its simplicity.