I also have a couple of Alien Bees and I love them. However, I now realize that I can do basically the same things with lighter equipment using speedlights.
Inexpensive studio setups are great, I got the Alien Bees primarily to shoot black belt photos for my martial arts school. But setting them up is a PITA, and unless you always work near outlets, you have to buy or DIY battery packs for them to work outdoors. I will pull the AB units out only rarely because my family doesn't want to pose for me and you're not going to drag the ABs to parties and family gatherings.
Having gone through the strobist.com Lighting 101
and then going through all David Hobby's onsite descriptions here ...
http://strobist.blogspot.com/2006/03/on-assignment.html
I would strongly suggest you start with speedlights. I say that given your budget, and the fact that you will want more photos of your new baby than the typical naked-on-a-bear-skin-rug shots. In a home studio setting, you can do absolutely everything with speedlights you can with monolights, but I think you'll find yourself wanting to capture nice shots of the baby at the playground, with other kids at other homes, chasing bugs in the yard. Your desires will go way beyond posing the kid in your 'home studio'. Trust me. And anywhere other than your home studio, the speedlights are muuuuuch better to have than the monolights.
Don't get me wrong, I'm not making a "this is better" suggestion, you'll eventually want both. Studio lights are much fun, I would not trade my ABs for anything. But I will not get more. I have two of them, now I am trying to put together a 3-speedlight setup that can be used anywhere (2 lights to start and I could be busy and challenged for years), and if I need a hair light or background light in the home studio, I'll use the speedlights along with my two bees.
But having been married for 25 years, I can tell you that if you get the studio lights, then when the kid is running around all over the place and you tell the wife now you want a set of speedlights, you will run into, um, shall we say, resistance? 
I suggest the way to go, for what you are describing, is a set of two speedlights with stands and modifiers now. Use them both out-and-about and in your home studio. As your skills improve if you want them, get some monolights later. It's not an either/or, but a first/second decision in my mind. You will get much more versatility out of a speedlight setup than a monolight setup. I'm not knocking monolights, they are great. But that really is not an opinion, it's a fact. I mean the versatility comment is a fact.
There are some things monolights will do better, but there are things you will do with a speedlight setup you'll just never do with monolights (not that you cannot, but you will not). It's a fact that you will spend a ton more money getting power packs and find moving them around a ton more hassle. I think you are much more likely to use a speedlight setup a heck of a lot more and end up with many more memorable shots of your tyke as he/she grows up with the speedlights as opposed to the monolights.
Eventually, I think you'll want both. But get the speedlight setup first, you won't regret it. I strongly suggest you run through this from start to finish, it will take about an hour. It will amaze you.
http://strobist.blogspot.com/2006/03/lighting-101.html
Good luck regardless of what you decide!