It seems like a "duh-uh" and others have mentioned it, but it's important enough, imo, to say it again . . . while the time commitments may or may not be great, having animals can limit your freedom. If you have chickens, you may be able to leave them for a weekend with lots of water and feed (assuming they're in a fenced area safe from predators), but with any animals that require milking, you've got to do it twice a day. Period.
While we could leave our chickens for a day or two, we can't leave the horses. We have a geriatric horse that has to be locked up twice a day for one hour each to eat. He has few teeth and is a slow eater--the other horses will steal his food if he's not locked up.
This weekend my husband and daughter are taking off to Charlotte to see a basketball game. I'm staying at home to care for the animals. When we went to Florida for a week, we were fortunate enough to have our neighbor feed the animals (and we returned the favor the past week). Before our neighbor, we paid someone $30 a day to do it, but he became unreliable. Finding someone to do it--at any price--can be difficult.
The time commitment for chickens once you get things up and running isn't too bad. Depending on the weather and your facilities, you're looking at anywhere from 5 - 20 minutes twice a day. We have tried automatic waterers without much success, so we had to stick with the metal waterers, which takes time to rinse and refil when you're looking at 6 of them. (Yes, we have more than a few chickens.) Feeding is a snap, though. I can't imagine leaving the chickens over a weekend in the dead of winter (frozen water) or the heat of the summer (not enough water), but the spring and fall I could see leaving them for a day or two.
I'd start off slow with animals that don't require too much effort. Then you can get an idea of whether or not you like the life. We've got way too many chickens right now, primarily because we're raising some for meat. The kids got sentimental early on, but now they're busy eyeing the chickens to see when they'll be ready for butchering (and their workload will be reduced). We have about 50 right now, and will get down to 20 after butchering, 5 of those being left being cute bantams that my youngest treats as pets and which aren't good for meat or eggs.

We have four turkeys that should be in the freezer in a couple of months, and life will be far more manageable. 50 chickens create a lot of poop and mess.
Oh, we do keep the turkeys and chickens separate. I know some have kept them together with success, but I've heard enough horror stories that I'd prefer to keep them apart.