Cattle require a lot of acreage per animal if you are going to depend on grazing them vs. feeding them hay year round. Depending on your area of the country/climate, that could be as little as 5 acres per head, or 100+ acres per head.
Some climates require that you feed hay in the winter (or year round), and cattle can eat LOTS of hay. They also produce an equal amount of manure, so you will need a way to handle the manure. You can use solely small square bales, but if you have say, more than 4 or 5 head of cattle, then round bales are a lot easier and more economical to manage. Feeding round bales can require specialized equipment (i.e. tractor with bale spear, bucket, pickup bed mounted bale spear, etc.).
Fencing definitely IS important. It needs to be strong.... If the grass is greener on the other side, the cattle will find a way to get to it. You will also need an area with super reinforced fencing to "work" the cattle: seperate/treat sick ones, vaccinate, worm, load/unload etc. You can make do with 6 or so heavy duty pipe corral panels, depending on how many cattle you have. But the more head you have, the larger and more specialized your facilities need to be.
They do need shelter, and it doesn't have to be fancy. A good close stand of cedar trees can be sufficient, but a run-in shed is nice, also.
They drink A LOT of water. And they will need access to it 24/7/365. So you'll need a heater for below freezing. And running water (like in a hose!) sure beats the pants off bucket-brigading it from the house.
Vaccines depend a lot on what you intend to do with them, and where you live. You'll also want to get educated on parasite control. A local cattle vet or county extension is a great resource for that info.
Yes, they can get sick. It can be a simple fix, or it can be a long expensive ordeal. One thing to keep in mind is that most large cattle operations are in it for production and income. Therefore, they do not sink thousands of dollars into veterinary care with questionable results. If the animal cannot be "cured" to the point that it can be fattened up for sale or bred, then it is culled (generally taken to a sale barn). I've seen all sorts of cattle illnesses - from bloat to uterine prolapses to water bellies to foot rot to lightening strikes to mastitis and on and on... I have, cough, cough, sunk several thousand dollars into my "pet" Hereford....
Breed wise.... Well, you can get into LOOOOONG arguments with lots of people about what breed is best. Many people are very loyal to "their" breed - much like sports teams, car manufacturers, etc. You need to get what works best for YOU - what fits on your acreage, what temperament, what size, polled vs. horned, what your intended use is. Be aware there are "flippers" out there - people who buy cattle at local sales and then "flip" them for a higher profit. So watch out for Craigslist ads - look for clues on the property. Personally, I am partial to Herefords (full size or mini) and Dexters. I actually prefer the Dexters more because their temperament and milk production.
Polled cattle are nice for beginners - they give you a bit more confidence in your safety. But horned cattle are fine, also. They don't gore other cattle or animals, but you can accidentally get bumped with the horns... Dehorning is best done when the cattle are very young, though it can be done up to a certain size. But the larger the horns, the more gory the procedure. As in - horror movie, spurting blood, huge caverns in the skull - gory. We waited too long to dehorn ONE TIME and we'll never do it again. You can pay more to have "cosemetic" dehorning done, and it is much less gory, but cha-ching - you don't want to do it to a herd of 100. $$$$$
Your cattle will need to be transported on occasion. You'll need a way to haul them yourself, or a way to hire someone to do it for you. Finding someone to haul onesie-twosie loads can be challenging. Don't expect to be able to haul them in a horse trailer, either. Some horse trailers CAN be used, but many cannot - they are too small, the dividers and padding gets damaged, the doors/ramp are not compatible with the chutes at the vet/processor/sale barn.