Cutting concrete it easy....with the right tools. If you do in fact have a six inch slab, you can forget the angle grinder and circular saw suggestions, neither one will come close to cutting through the slab. (If you had very little cutting, like a 12" x 12" small area you could get by with a circular saw but it would be dicey.); you need something that will hold a 14"blade and has the power to turn it in concrete. You will need to rent a concrete saw; you can either get a hand held cut off saw, or a walk behind saw. If you aren't well experienced with power tools and pretty strong I don't recommend a cut off saw. It's basically a motorcycle motor with a blade attached to it. Pretty dangerous in the wrong hands. I have personally seen grown men carted off in ambulances due to kick back.
If you do go the concrete saw route, you may want to look on ebay for a blade like
http://www.ebay.com/itm/14-Inch-Dry-or-Wet-Cutting-Segmented-Saw-Blade-for-Concrete-and-Brick-1-Arbor-/150848068406?pt=LH_DefaultDomain_0&hash=item231f3edb36 Pay attention the the arbor size of the saw you are renting. Most rental places won't rent you a blade, and they have an absurd mark up on consumables like blades. Expect a concrete blade at the rental store to be 150-200 or more.
Make the cuts in the concrete about 1.5 to 2 inches deep per pass. Trying to cut the full depth is a recipe for failure. Take your time. Most walk behind saws have water hose attachments that will keep the dust down and extend blade life. (oh yea, the rental house might have a cart for a hand held saw; I would let price be the deciding factor if that's the case.)
As far as a jackhammer it just depends how much you have to remove. A large sledge hammer will do the same job. Me/my employees have demolished thousands of square feet with one. It just depends how much you have to do at once. Get the biggest one you can lift; not one of those toy 8-10 lb hammers. Electric jackhammers are the next best thing and you should be able to rent one where you get a trencher and saw. Weight is your friend; get one that weighs at least 50 or 60 lbs. If you really have some concrete to remove you need an air powered 100lb hammer with a portable compressor that has enough cfm to run it. You shouldn't need one that big.
As far as the trench; 70 feet can be a lot or a little depending on your soil. I can tell you where I live in GA, that is more than I would personally want to do. But 150$ is a lot for a trencher. (plus most rental houses have loads of fees on top of the advertised rate.) A good man could dig that with a mattock and a trench shovel in a few hours. You might consider hiring a laborer, a real laborer not some kid, for a day at around 10 or 12 bucks an hour and let them dig the trench and help you bust up/cart off the slab. It would be 100$ well spent if you have someone who can really work.
Pex isn't popular in my area so I don't know, but make sure whatever you are putting in the ground is rated for underground use and will pass inspection. Also, some municipalities like to see the pipe in the trench uncovered for inspection, so bear that in mind as well. Ask your building dept.