Very good question. In general (I'm sure
joberg can elaborate further), the type of suit and shirt you wear determines the kind of tie you wear. If your jacket has a wide lapel and your shirt has a wider collar, you want a wider tie. A narrow lapel and narrow shirt collar would require a narrower tie. As far as which knot to tie, that's generally also determined by the width of the collar and somewhat by how far apart the collar opens in the front (the upside "V" if you will). If you have a wider collar, you want to tie a bigger knot like a full Windsor. A medium size collar would call for a half Windsor or a four in hand knot. For narrow collars, something like a Nicky knot would look nice.
As far as colors, your tie should be darker than your shirt (unless you're wearing a black shirt of course). I like to wear ties that have some kind of textured knit to them rather than the typical silk print ones. As far as patterns, in general you should mix and match between solids and patterns. You might hear that you shouldn't wear a striped suit, shirt, and tie together, but I've seen it done and done it myself. It can absolutely work but it takes the right style of suit and shirt to pull it off. I always like to wear a pocket square too (not a handkerchief, that's a different piece of accessory with a different use). Now, a lot of men like to wear a matching pocket square and tie, but it's considered a no-no. I happen to agree with that and I never wear a matching set myself though it doesn't really bother me seeing it either. It's very low on the list of fashion faux pas. It's typically a thing you'd see in a ceremonial setting like something groomsmen would wear for example.
As far as "scarf" ties and ascots, I have no experience with those haha. Mr. Furley could sure rock them though. I've never worn a bolo tie either, but I've heard if you do wear one your testosterone levels triple just from the sheer manliness of them.