I have a 2001 LS with the suspension package, 6-speed, and ABS. I think that it feels a bit mushier than the 99-2000 models with the package but that is probably due to the added weight and 16' wheels/tires. I noticed a bit more lean in the turns in the 2001 than I did in the 99-2000 as well.
I did not drive a 2001 without the package though. The suspension package does make it a but firm and some people do not like it if the Miata is going to be their daily driver. I would say for most people, the standard suspension is just fine and it still handles great.
I actually put lowering springs on my 2001 to help flatten it out a bit in the curves and to get rid of the gap in the fender wells. You can take a look at my pictures to see what this does.
http://albums.photopoint.com/j/AlbumIndex?u=1208127&
a=10648114
I like the suspension package and would suggest getting it if you really want to have your Miata handle even better than normal right away. However, you can always upgrade the suspension later, but my dealer was able to get all of these features on a silver LS so I was lucky.
Good luck