Jack hammer
I remember helping a friend dig in his yard in your area... We started with shovels, then picks, then ended up renting a jack hammer. I wish we would've started with that.
Do you have six mile soil and tons of shale? If your soil is that hard, the tiller may just spin on top and beat the hell out of you.
You may think its silly but renting a small jack hammer to get started will save you tons of hours of labor and sore muscles and blisters. Plus, if you're like me, its fun to play with that kind of stuff.
Regarding your mulching with cardboard base - if you plan to put flowers or plants in eventually, that is a good approach to cut back on weeds. We've used fabrics in the past as well and we found that newspaper and a thick application of mulch cuts back on weed growth as well. However, when you do plant, you will want the soil below it to be real loose. Otherwise, the plants roots will struggle to dig in.
the key to a good landscape bed is a good base for plants to grow - Bust it up, add bags of menure and then till it, then add your cardboard & mulch.
Good luck!