I feel your pain!
For digging, nothing beats serrated-edged shovels. The shorter handle works best for me because I can push the shovel with my foot and lean down on it to add my weight. Check these out, they're pricey but last a lifetime, and well worth the investment:
In the spring and fall I work a few inches of compost in to amend my soil. I also add compost whenever I plant something new. Some spots in my garden are wet, and I add Perlite for extra drainage.
I've had to pull up so many plants that couldn't thrive in my garden, but over the years I've been particularly successful with spirea, ninebark, nandina, Royal Purple smokebush, Japanese Maple, hosta, Japanese willow, inkberry, boxwood, barberry, sunshine ligustrum, cypress, roses and hydrangeas in some spots, juniper, pines and hollies (which I amend with Peat Moss to acidify the soil).
Gardening in clay is a real challenge, good luck!