This was my very first woodworking project. It didn't end up perfect, but I learned a lot by making it, and it is still a quite nice dining table.
The minor modifications I made of the plan: I used 1x4-s as a frame for the table top, flush with the top. (The 2x2-s are next to it inside.) I made the lower supports out of 4x4-s (except that they didn't have 4x4-s at the store here so it's really 2 2x4-s put together). I have a few 2x4-s connecting the 2x8 and 2x6-'s in the base, to make it a bit more stable (not sure I really needed these but anyway), and I also ended up putting a few 2x4-s in the core of the base, again to make it a bit more robust. I routed the 1x4-s on the table frame, and also the table legs with a 45 degree bit (using a router is really fun! And really easy).
I used pine for the base and red oak for the table top -- mostly because I have oak cabinets in the kitchen. After sanding to 150 grit, I stained the oak first with Minwax Oriental Ginger (I would have used a dye if I had had one but this worked fine), and then two coats of GF antique oak. The Minwax gave a nice warm orange undertone while the GF highlighted the grain. It has 6 coats of GF high performance water based poly on it, sanded and wet sanded with very fine grit (up to 2000) so it's pretty smooth. It looks like many people use grain filler with oak, but I like the grain so I didn't. The base is painted white with whatever semigloss white paint I happened to have at hand.
Lessons learnt: 1) always, always measure twice, and always, always make sure that everything is square. 2) Don't build a table base from a board that's not absolutely straight. 3) Make sure to have enough screws and that the screws are of the right kind. 4) If you use a 45 degree router bit, you need to sand that 45 degree part much finer than the other parts of the table top, otherwise the grain will stick out and make it very rough. 5) Don't wet sand oak -- the poly dust white residue gets into the grain and it's impossible to remove.