Welcome, Andrea.
Your best bet, unless your existing fish are very old, is to increase the size of existing shoals in the first instance - shoaling fish such as tetras do best in groups of 6+ of their own kind (ie black widow tetras being one kind, cardinal tetras another) but the more, the better, as they'll display more natural and interesting behaviour. For example, unless your black widow tetras are quite old, you could increase their shoal size to 6+.
Once you've decided whether and by how much to increase the shoal sizes of each of your black widow tetras and cardinal tetras, then you can focus in more on what other type of fish from your wish-list to get. It's best to get fish that suit your water type - put your postcode into your water/utility company website and find out and let us know what the various readings for hardness are (eg in degrees Clark, German or French measurements), and we'll be able to advise further on what would work best ie thrive best in your aquarium. Seriously Fish, which Sue refers to, gives specific details on suitable water hardness levels - but you may need to translate your unit of measurement into the ones used there.
Hope this is helpful. It's all very exciting for us to read about your tank resurrection and get involved in helping you transform it into a work of wonder.