OP, this is a very difficult question for anyone to answer here..every airline is different, it's all based off seniority/contract...
I'm at RAH, and I can tell you, I'm home more than I'm gone. I'm sitting reserve in Pittsburgh and flew only 5 days last month, but usually I fly a little more than that. If I wanted a line, I would be gone a lot more obviously.
What WILL change is the fact that you don't know your schedule more than a month in advance which makes it difficult to plan some life events..you can obviously bid the days you want off but nothing is guaranteed especially when you're junior. As for vacations, at my company you get 2 weeks but you have to take the full 7 days at a time twice a year-you can't split your vacation days up really and the dates you request are all based on what you can hold seniority wise.
Overall, between my experience and my friends at other airlines, you should have more free time than someone with a 9-5 m-f job, and for the most part people that don't are choosing to work extra. Do I get burned out some months, yes, but I know I have a lot better schedule than someone that sits in a cubicle all week-even if I had a line. Usually given 2-4 days off at a time, and those are your full days off-don't have to bring work home with you! Good luck!