http://www.nrcs.usda.gov/Feature/backyard/terrac.htmlYou could use the same stone as you have for continuity, or use treated wood.
Since your going through all the trouble to double dig it really isn't that much more work and will end up giving you a much better garden space. My best price for your type of stone is about 80 cents each, so it ain't cheap but think of it as an investment. The more you work and water that "hill" the more it will run off into the grass. The Ivy is whats keeping it where it is now and no amount of vegies will hold that soil in place like the Ivy does.
3' terraces let you reach your plants from both sides {the stones are your path} and keep you from walking IN your beds when planting and cultivating.
I would start from the top down and add at least one row of stone at the bottom. Use weed barrier behind the stone to keep soil in and weeds out. Your DYI center or stone supplier can help a lot and give you step by step instructions.
http://www.nrcs.usda.gov/FEATURE/backyard/pdf/terrace.pdfAs far as seeding directly into the ground it all depends on the plant variety. With the amount of work you've got, go with seedlings this year. You've got to get some satisfaction from your work this year or you could get discouraged.
ps. Understand that the more you dig around the more weed seeds you stir up. If it were me, I'd fry that Ivy with Round Up and be done with it. I know some poo poo "poison" but a hard 1x hit of chems will save you DAYS of work this year and more time later. Ivy it hard to eradicate and it can take all the fun out of gardening to fight a plant that just keeps coming back.