Most kinds of food are fine. The biggest problem is lessened bite strength. A badly overcooked steak would take forever to chew, and I find biting into apples too difficult now (though cutting them into slices helps, but chewing the skin is very difficult). So, very tough meat and apples are the two biggest things for me. It also takes a little longer to chew - not drastically, but enough that if you're a fairly quick eater, like I am, and you don't take your time, you might not chew things like pasta quite long enough, which can give you indigestion.
Some things I eat regularly with zero problems whatsoever:
Burgers
Potatoes (in any form, including chips/crisps)
Meat (chicken, pork, beef, anything really. I can eat steaks, but I wouldn't subject myself to an overcooked one)
Cooked veg
Fruit (bananas, strawberries etc. I only avoid the aforementioned apples)
Avocado
Pasta
Bread, sandwiches, toast, cake, pancakes, pizza
Chocolate (it does get stuck to the roof of the upper denture, which is annoying and ruins some of the sensory fun of chocolate, but it's still very enjoyable. Sticky/chewy candies are less enjoyable as they do just get stuck to the denture, but sometimes I eat them without dentures in when no one else is around haha)
As you can see, it's not very limited at all. As for how long it takes to get used to, it doesn't take terribly long. In the period of healing after extractions, your gums change shape a lot, and the dentures can become loose, which can be more annoying. But once you have your permanent ones, it's all fine. I rarely think about them now.