You need a cat.... keeps little critters such as mice and rats down... and they WILL find any feed you keep around for any other animals.
Chickens... both eggs and meat...interesting activity....can be caged or let them run about, or both. These would be my first animal. Small, can be handled/caught with reasonable strength and skill. Set up a place for the hen to nest and raise a brood. Little chicks are cute to watch. Chickens are a pain to pluck, but if you scald the feathers, they come off easily.
I recommend chickens..you can learn things from your neighbors and this is important since you are new to this. There are many, many, many kinds of chickens.... you will learn much studying up on them...meat breeds, egg layers, fancy feathers, green egg shells, amazing stuff....
Watch Craig's List...often people, particularly around Easter, get chicks and bunnies but then they grow up and people want to get rid of them...for free...you could get your start there, breed these, and see what happens,
"Spanish goats" ...those with long ears, various colors, big bags, etc. would be my next path. These are a combined milk and meat animal. Very often the does will have twins or triplets.... a couple of times a year...so, productivity of offspring is high. Goats will quickly learn to follow you around..into pens, etc...I would leave the horns on the does...they make good handles...take them off of the Billy...they are larger, stronger, can be a safety problem made more dangerous with horns. Fear not about the milking situation... you can milk the goat or not.... young kids cannot take all the milk the nanny will produce...so if you take some, it does not matter. Yet, when you go on vacation, the kids will take all the milk...so, no health problem presented at vacation time. Management is the key... put kids in pen away from nanny at night.... milk her some in the morning, then let the kids nurse her dry, then separate them for the day...repeat at night. There is NOTHING cuter than a baby goat.... trust me. You will need some fencing to keep the goats at home and not visiting the neighbors too frequently.
You can make a milking table....the goat will learn to jump up on it, presenting the bag at exactly the right height for you to milk... better for your back....Lots of flexibility with goats...they eat a wide range of browse or store bought grain...... your choice....they eat well...called cabrito in spanish... a delicacy
Pigs..stink...I would NOT suggest you mess with them.
Rabbits are quiet and productive.... eat good....easy to skin and clean. Again, recommended because you can learn from neighbors.
Am glad you are NOT wanting to make pets of your animals...they are for food and fiber only....agreed....if you are not familiar with slaughter techniques, best you find out about them... no matter what animals you select, there will be blood, etc. involved with slaughter and cleaning and preparing for the table...but not too hard to learn or do once you gain a little experience.
Stay far, far away from anything exotic... emus, llamas, etc.... stick with small and easy to handle and house and care for...and inexpensive...On two acres, you do NOT have room for cows, horses, mules, donkeys, anything large.
I suggest that unless your property is very productive you start off with no more than 4 nanny goats...if you can find somebody with a buck you can borrow from time to time..GREAT...they are large, stink, can become somewhat difficult to handle.
Slash Pine is right about guinea hens...watch dogs and broad foragers. Meat and eggs.
Quail, IMHO, are temperamental to raise. Various problems need to be understood to be successful...of the animals mentioned so far, these would require the most cleverness and attention on your part. Best you get good at chickens and rabbits first, then graduate to quail. That said, quail is my favorite bird meat and right up there with shrimp IMHO.
