first of all I want to say GREAT CHOICE on breed! I raise and show three breeds of rabbits, Satins, Mini Rex and Mini lops. I like different things about each breed, but I love the personality of my mini rex. My buck has such a personality, he is friendly and likes to have his head petted in between his eyes. He will come hopping up to you during his exorcize time. My doe is also active and friendly. She would rather not be picked up, but will happily come over to you for petting and treats!
That said there are some things to watch for. First of all I recommend buying rabbits with pedigrees, preferably from someone who shows. (some hobby breeders are awesome, others are just trying to make a quick buck). I like to see where the rabbits are housed, or at least pictures of where the rabbits are housed depending on the distance, before buying a rabbit. Since you plan to breed I suggest checking out this site
http://mr-colors.tripod.com/ Unlike some breeds you have to be careful what colors you breed together or you can really get some bad markings and rabbits who will be disqualified because of color. You may not plan to show, though you should try it, it is so much fun,but you will have more luck selling your babies if they are show quality with no DQ's.
Take it from someone who did it the hard way, do it the easy way, Buy as high quality animals as you can from the beginning. Don't cut corners on the cost of the pair. I made this mistake with my Mini lops and am having to start over almost from scratch.
Mini rex do have a few health problems to worry about. They have more back problems, and especially as young kits can sometimes jump and twist wrong and injure themselves. We have only had this happen one time, but upon researching it have found it happens more frequently then I would of thought. They can also sometimes throw peanuts (babies who are much smaller then the others, more then mere runts) these babies rarely live longer then a few days and never survive to weaning. This is from the dwarf gene, something that happens in all dwarf breeds.
Here are a few pictures of ours. I am wanting to add chocolate and blue otters to our heard this coming year. I saw a Chocolate Otter at the last show and fell in love with him. When I was little I had blue and Opals, which was a nice combination as it gave at least some variation in the litter colors.
From my first litter with this buck and doe a broken black silver martin kit! Wasn't a recognized color then, but now it is. When/If they throw another I am keeping it!
This is the cage we use for our does ( it is a three row compartment with an inch spacing between the cages to prevent nipping each other) In the summer we keep them under a large area of trees in the corner of the yard, in the winter in a barn/garage with heat lamps (when we have little babies, and to keep the water from freezing when it gets really cold).
Good luck and have fun, if you have any questions feel free to ask!