You suspect the wood is air dried. Before you get too involved in the project you might get a moisture content meter to check the moisture content. If the wood has a too high moisture content you can expect more wood movement than you are accustom to. It would be a shame to use up some nice wood and have it warp and crack later on after the project was done and finished.
When I finish wood with knots I normally mix some bondo with burnt umber tinting color to the color the knot will finish and fill the imprefections with that. Bondo won't accept any color once dried so you have to mix the color before the hardener. The colorant is a universal tinting color like paint companies use to make paint. Sherwin Williams often sells it in bottles under the label Caltint. If they are nice you might ask them to put some in a empty can for you. Sherwin Williams doesn't have burnt umber in their machines though. There you would have to get raw umber and red oxide and mix it together to make burnt umber.
As far as finishing if you are building a formal piece of furniture then it's traditional to fill the grain so you don't see the texture of the wood in the finish especially on a table top. It's a personal choice thing. You might put some grain filler on one piece of scrap and some not filled to see if you like it. Also going with tradition if it's formal the knots should also be removed.
The finish if you don't have the means of spraying you would have better luck using a wipe on polyurethane. A table top shows every defect so you don't want to have a bunch of brush marks to work out. If you do have the means of spraying, I prefer to finish with pre-catalyzed lacquer. It's easy to work with and dries quick.