Hoe vs Tiller

We have a 15ft by 26ft garden mapped oit right now and I was wondering which toll would be more effective at removing what is there right now.

It's completely flat. No stumps or left over plants besides the grass.

I planned to get it dug out maybe 2 inches and put weed protector then mulch down and the raised beds on top.

Any advice is helpful! Garden is in Centeal Texas.