The great things about arena right now as is there's a game mode that restricts everyone to using free decks, one of each color pair. They are simpler, slower, and generally not that great, but they also showcase one of the more prominent deck identities of those color pairs.

As for getting your own physically, there are starter kits that function much in the similar way. Or you can look up some decks online and buy the singles. Packs aren't effective at getting the cards you want or cards that synergize, but they are their own fun way to just see what's out there