x's 2 what Aaron said.
If you do it in sections, get some expansion material (felt, neoprene, ect tra) at your local supply and install at each joint before the next pour. (easy)
If it where me though, I would save up to do the whole pour and hire a crew for the finish, or as Aaron said rent the float. Bull float can be had for less the $20 a day most of the time.
Allot of concrete contractors will do the pour and the finish for $1-$2.50 a sq ft. Worth calling around. All you do is the prep, forms and steel.
With no footer, your looking at around 7.5 yards of concrete, I just paid $79 a yard up here in DFW, so probably close to the same in your area.
Using a "mixer" would sure be a labor of love