There's no reason not to start with eggs although you'll have to make sure that any breeding stock are unrelated.
As for incubators, they aren't too much money to buy the cheaper models, gaging from the rental prices in the UK (where I am) you may as well just buy one. You can however make one realitvely inexpensively and there are various designs online. The cheapest I've seen, design wise was using a styrofoam box (often you can get these for free in pet stores - they are used to transport tropical fish). Wiring a lamp through a thermostat set to the correct temperature (so that the light will turn off when it's warm enough and switch back on when the heat dips. And put a couple of bowls of water in there for humidity. You'd need a thermostat, a lamp, a box, a sheet of glass (you'd cut a hole in the side of the box so you could see what's going on in there), two thermometers, one to use for temp and one to use as a "wet bulb". Heck, check out this link - explains it better than I can:
http://www.cyberquail.com/incubators.html
As for eggs, depending on species, they can only be stored for 7 days and you need to turn them daily, and store them either on their sides or pointy end down. Once you start the incubation process, you need to turn them at least three times a day. I'm not sure why but apparently you can turn them more frequently (I think as much as once an hour) but it has to be an odd number of turns.
Hatching chicks is so much fun. I had a broody do it for me last year but this year I've got an incubator going
Can't wait for D-Day