Broody hens have a higher hatch rate than inexpensive incubators, provided that they stay broody, and usually they do.
If you have a broody hen, she is auto-turning, she modifies the humidity herself, she decides which eggs are no good, she is a brooder as well as an incubator, she teaches all the chicks to drink and to feed, and she can usually deal with predators.
However, a hen will not become broody just because there are classy eggs at auction, or because you have done your maths and decided it is the right time to set eggs so that your pullets will start to lay in autumn and continue through winter.
I feel fortunate to have hatched eggs both ways because you learn different things. I am glad I began with broodies, because they do do a lot of the worrying for you, and that counts for a great deal the first time.
ETA: You can't get Lil Giant Incubators here and I have no idea if they are inexpensive or not, but in my experience most people consider an inexpensive one first when they are weighing up the options. Should you be looking at the Rolls Royce of incubators, please forgive me, and don't assume I was calling you cheap!