A table runner sits as a strip down the centre or length of a table, on top of a bare table or a table cover - it's meant to be seen, not to protect the whole surface, so the fabric choice is mostly about the look and occasion rather than durability.
Velvet and lace runners are usually the most decorative and least everyday-durable - they're the ones to bring out for a festival or a dinner with guests rather than daily use. Jacquard sits in between: it has a woven-in pattern rather than a printed one, so it holds its look through more regular use, which makes it a good pick for a dining table that gets used often but still needs to look put-together. Cotton is the simplest, most washable option for a table that's in daily use.
A runner is meant to leave the table visible on either side - as a rough guide, an inch or two of overhang at each end looks intentional, while a runner that's too long for the table starts pooling awkwardly.
A runner works over a plain table cover or directly on a wooden/glass table - it doesn't need to match the cover exactly, a contrasting texture (like velvet over a plain cotton cloth) usually looks more put-together than matching fabrics.
Cotton runners are machine washable. Velvet, jacquard and lace hold their finish better with hand washing or a gentle machine cycle in cold water, and are best air-dried flat rather than hung, so any tassels or sequin work don't pull out of shape.