First time garden looking to plant tulips and looking for advice

Recently moved out of an apartment and into a house so for the first time I have a garden. The garden is pretty big but is currently just grass, so looking to add some colour to it. I can’t decide whether to go for pots or dig up some of the grass.

From what I have read, it’s almost time to plant tulips and I think tulip flowers themselves are quite nice, so I have some questions.

Is it literally just a case of buy some bulbs, put the pointy end facing upwards, cover them with soil and then in a few months they will start coming through? Is there any maintenance around plant food/watering that need considering?

Where would you recommend buying tulip bulbs? And pots if I decide to go down the growing in pots route.

Are there any other things I could plant over the winter? Either other flowers or even bigger things like bushes/trees?