Hi,
Congrats on your new house and your impending ownership by a cat 
First of all, I would highly recommend asking your vet (if you don’t have one yet, ask around for a recommendation) on where they would go to adopt a cat. We have several shelters locally and there is one at least that seems to have more “heartbreak” adoption cases- whether its due to volume or poor disease control , I don’t know.
So what else should we know?
- What procedures/surgeries/vaccinations should we insist upon?>>
Distemper, Rabies, Fel. Leukemia should be done, preferably not for the first time when you are walking out of the door with the cat. Should be spayed/neutered and Fel. Leukemia/FIV tested as well (expect to pay a fair adoption price for this).
I think its individual preference, I love my boy kittys- they tend to be more cuddly and sweet in my experience. Females can be a bit more touchy about petting and generally are more independent. Really though- pick the one that picks you!
- As young a kitten as they can give us in good conscience, or a few weeks (or months) older?>>
I wouldn’t get too stuck on age- what I would look for is something that looks extremely healthy and active. Watch out for runny eyes/nose, sneezing , skinny , etc. That being said, I picked a scrawny kitten with a bad eye when I adopted from a shelter and he turned out great (I had no choice, I tried to pick a healthier looking cat but Wily demanded that I take him home). If the shelter offers a complimentary exam at a local vet, take them up on that but wait a few days first. Cats in shelter situations often get Upper Respiratory Infections, mostly not serious, but will probably need some antibiotics. Give that bug a few days to cook (unless you notice symptoms right away) and you will save an extra trip to the vet (make sure you budget some money for meds).
Once we get a cat:
Mostly watch for string/small items- kittens like to play with string and can get in trouble with that. Make sure kitten has its “happy place” where it can get away. Scratching post and safe toys. Also, kittens like to to squeeze into small spaces, unfortunately have seen a few times where they have gotten into recliners and gotten smushed
.
Extremely easy compared to housetraining dogs. If the kitten is very small, make sure its easy for them to get in. Show kitten the box, possibly confine kitten near box for a day or two until he/she is routinely using the box and thats about it. Keep box clean, cats will be picky about this!
I prefer dry food, once the kitten is 8-10 weeks old, canned is not needed. I used to be anti-treat in general but when my Wily got hyperthyroid and had to be given pills twice a day,I realized how lucky I am that he is a whore for treats/food :). So now with my younger cat, he gets a piece of Wily’s Pill Pockets every day so if he is ever sick, no shoving pills down his throat.
Be prepared to enter a state of slavery…