Fastest Handbrake rips will be with the quad core server model, but none of them are bad choices.
To put it in perspective, the base model mini is essentially the same as the 13" base model MacBook Pro. On my 13" MBP I can rip an average length movie in about 35-40 minutes.
On my quad core mini server, it takes about 20-25 minutes.
Whether that is worth another $350 (because you absolutely must add RAM to the base model) is up to you.
If you're going to be ripping DVD's constantly, then you probably have a large collection to go through and the speed will be worthwhile. Having the two, faster, 500GB hard drives built in already is also helpful for a media server.
It will also be helpful for future use, as at some point you may decide to use an external Blu Ray drive and rip from those. Converting those files in Handbrake will be more time consuming than standard DVD's, and you'll be thankful for the speed boost if you ever decide to do that.
For your purposes, you will want to pick between the base model or the server model. The $799 one with the GPU may be good for gamers, but it will be useless for your needs, and the processor isn't going to be noticeably faster.
I have over 50 kid's movies ripped/encoded and I'd bet each has been watched well into double digits.