Oil based semi gloss is a good finish for a table. Oil tends to be longer wearing and stands up to abuse better than latex. It does take a bit longer to cure. Don't subject it to hard wear for at least a month.

To paint a dark colour like black, use a deep tinted primer. Otherwise you will have a hard time getting a dark final coat. The kind of primer to use depends on what is on the surface already.

If it has been finished, especially with polyurethane, you will be happiest in the long run if you sand down to bare wood.

Technique depends on the look you want and the equipment and experience you have. If you are an experienced spray painter, it can be easier to coat round legs this way. A good spray coat can have a flawles, factory made look. But a brush finish gives a hand done, antique look, that won't happen with spraying.

I also plan to paint my kitchen table and 4 chairs black. Thanks for advice re type of paint to buy. My table is from Rooms to Go and is a pedestal table with inlaid dark green tile. I can't stand the colors anymore and want the whole thing black (tiles and the wood). Currently, it is light pine/hunter green contrast(backs of chairs, chair legs, tile and pedestal are green) What do I need to know about painting tile so that it lasts? I would love to not have to buy a new set.

Here is a link that might be useful: My breakfast table and chairs

P.S. I forgot to mention that this is not solid wood, only wood veneer. Can it still be refinished?