AD, come right into the best addiction you'll ever have!
A couple of words of advice.
#1: Your wife needs a mentor. Find a local BK club & join & attend every meeting
#2: GET A LOCAL MENTOR (just in case you missed that advice)
#3: with the local club, see if they have an extractor. Many clubs 'own' one and everyone borrows it for free.
If I break it down, let's see. 4 hives, $300/hive for the bodies/frames, $1200. Then bees are $150-400 per hive (package/nuc/complete hive), let's say $250 each (nuc?) so $1000 there. That leaves $1800 for equipment. That's a little high, but it depends on what she is getting. Now another reason not to get an extractor now: unless you get intact good hives, you will not get any honey off the hives the first year!
But I will add, if she wants to do cutouts, it'll cost you.
I'd recommend getting a vehicle 100% dedicated to doing cutouts. It just makes it so much easier. Down here many of us just get a junker car/minivan & just leave everything in it, so we're ready to go when the call comes (time is critical with getting swarms). But if she's a newbie, she doesn't need to be at that level (but be ready if she does go that way). I will tell you doing cutouts is really enjoyable for many of us. Oh, a 'cutout' is when I remove a colony from someone's shed/deck/etc & take them home. "Free bees" are great, and you get really good genetics which matters.
As with Robin, I'm here to answer any questions. And you will have many. And if you missed it in previos posts, remember that 10 BK will give you at least 15 different opinions. Keep in mind my bees in Texas are different than by you. And other things are like the Ford/GM/Dodge debate: personal preferences.