What to 'buy' is a really difficult question for Wolfram language products.
At the "free" level is the Wolfram Programming cloud.
This will give you a taste of the language and you can do stuff. There are various levels of support, etc.
You could also look at Mathematica on-line. This is the equivalent of Mathematica in the cloud. There are some things you can't do that you can with desktop mathematica, but the advantage is that you can log in forming of your computers, and you can keep your files in the cloud.
This option gets pricey quickly, although your wife could probably get an educational plan which is a lot cheaper.
I am a long time Mathematica user, and I am used to using the desktop version of Mathematica. This is the most powerful option, runs without the cloud, and lets you do a lot more dynamic manipulation (since it does not need to go through the cloud to update stuff).
The downside for you is that this is a single computer license. However, I see that there is a desktop+on-line option for education that is inexpensive. The desktop-only version is $195, and the student versions are even less (one account for each kid is probably affordable). I did not want to click through to see the current pricing.
My suggestion is that you try the free options -- including a free trial of desktop Mathematica -- to see if this is what you want.
Your experience may be different, and my experience with the on-line versions is by working with beta versions, but I think that if you can afford it, the desktop version of Mathematica will provide a superior user experience for all but the most casual user.