Shane and Lou,
Ignore those whose feelings are hurt because people have chosen to learn how to do such projects as yours without the help of an overpriced plumber. Most contractors nowadays do cheap work just to make a profit. NOT ALL, MOST. Some contractors are very good at their job and are lifesavers.
Addressing your problem. I am not an expert at this but I too am currently relocating a toliet and a sink. My recommendation is to read up on clay pipe and pvc transitional connectors (like rubber couplings), DWV piping, etc…
my suggestion (SUGGESTION)
Measure everything out first so you cut at the right spots.
You will need to purchase a plastic TEE with the correct connection sizes. You will also need some ABS or CPVC pipe material which is the same size. You will need Rubber clamping couplings (Rubber connector with steel clamping bands). You will need some PVC cement clue.
First thing to do is using a grinder, cut the clay pipe where you want to make the tie-in. Next, clean the ends of the clay pipe. Now slip the rubber coupling over the clay pipe. Next take the pipe you bought and cut it so that you can insert it into your TEE and have about 4″ of pipe extended from both sides of your TEE where you will be connecting to the clay pipe. Use the PVC cement to bond the PVC pipes to the TEE. Let it dry for about 30 minutes. now you can insert your PVC to the opposite ends of the rubber coupling. Once this is all in place, tighten your steel clamping bands.
This is a recommendation not an exact how to.
Another option is call a couple of plumbers in your area and have them give you a free estimate. When they give you the estimate tell them you want it itemized so you can see what you are paying for (also so you can see the materials they are buying and how much their labor is). In addition, play dumb when they are there and ask them while they are inspecting what they are going to do. Most will tell you the process thinking that it is beyond you. If they tell you then you will have a better understanding. Let them know as well that you are shopping around so if you do decide to hire a plumber then they will give you competive numbers.
Last but not least check with your local officials to make sure the plumber does not have any negative complaints or how many. If you know someone who had used a plumber recently and liked them, use this plumber if he or she is reasonable. Word of mouth is always great especially with friends.
Hope this helps a little.