So, all the stuff that's faded out in the Start Game section? You get ALL of that for the $1 tier.
At $4, you get your saves stored on the online server, and also can make custom OC characters to play the game with. They can either start in a new world with you, or be found in the world as either unique passive encounters, or dangerous hostile encounters.
Also at $4 tier, you get the full Deckbiter game too, altho that is very rough at the moment. It's progressing slowly but surely.
If you aren't sure which tier to try, just start with the $1 tier and have fun with that new content. It's a TON of new stuff for just a buck. You can always upgrade later if you're having fun :)