What's a good base collection of tiles?
Looks like there are really two different questions here. Allow me to address the question regarding grooves on the tiles:


  What's the difference between tiles with and without grooves?


Basically, on tiles without grooves, the vertical edges run continuously straight from top to bottom. On tiles with grooves, there is a small lip at the bottom of the tile just large enough for a fingernail or a separator tool.

A visual comparison between the 1 x 2 tile without groove (red) and the 1 x 2 tile with groove (grey) shows the continuous vertical sides vs. the lip that forms the 'groove':





  Is the groove on the bottom?


Yes, it runs all the way around the bottom of the tile.


  Is one piece much more useful than the other?


The difference is mainly in the ease of removing the tiles once attached to another Lego element. As I mentioned above, the groove leaves enough space to prise the tile away from whatever other LEGO element it is attached to. In the case of the 2 x 2 Tile without groove that you reference in the question, according to bricklink, it was discontinued in 1978 after the 2 x 2 Tile with groove appeared in 1973, so I would guess that LEGO considered the 'with groove' to be a better design.