I have two recommended animals!
Small breed goats such as Nigerian. Do pay a teeny more for good breed line, it's worth it.
Nigerians are excellent milk producers with a rich fat content. Nubians, or other larger breeds will yield more, but per body size Nigerians have the most milk to feed ratio.
Goats do not eat much grass, not like sheep. They're browsers rather than grazers. There are many plants you can easily seed out your pasture with for goats (check your growing zone, but most forage does well anywhere.) It's always recommended to have good hay and balanced minerals and grains for feed as well, but pasturing the goats will considerably decrease their bought feed needs. Just a caution though...many goats are not on pasture. Should you buy a bred doe (my plan, I'm buying two because they are herd animals and need buddies) make sure to inquire about their feed. Changing a goat's feed suddenly can make them very ill, mostly the deal with all animals! Your goats will need an adjustment period to get used to pasture.
Nigerians tend to be lazier than big breeds. When people complain of escape artist goats, they typically have big breeds. Nigerians are homebodies and lazy. I love this, and think they're perfect all around for many small scale farmer's/homesteading.
Rabbits!
I received some of our surprise hens in a "coop" that I'm fairly sure was meant for rabbits originally. I'll never put more birds in it, terrible for them, but I think it'll spur me into having a small rabbitry.
Why? There are a number of breeds that are good multipurpose bunnies (meat, furs, and pet temperament.) I am only hesitating because, well, cute factors. I do think it is consciously harder to cull and process such cuddly little creatures. However, I do think that rabbits make sense on our homestead.
Rabbits can be put to pasture as well. Same concept as a chicken tractor, you can use rabbit tractors. Again, check with breeder, they likely need adjustment time and always keep grains and hay available.
Rabbits can breed every 90 days. Young can be harvested around 12 weeks. It is estimated that one buck and two does will provide 180 pounds of meat per year.
You could harvest some as meat, process furs,a sell some kits as pets or meat rabbit starters for someone else's rabbitry.
I probably wrote a novel here. Hope this helps!