Check what suspension you already have. GM rates its suspensions from mush to whoa in order of FE then a number (usually).
FE1=Ride and comfort (ie, mushy)
FE2=Ride and handling (more sport, less mushy)
I've heard and seen FE3 and 4 components, but none specifically for H body cars. I think Saturn ION Redline had FE3 as options, but couldn't tell you more about them.
Then you get into scary, the FE5. FE5 in H body form only came on the Bonneville GXP. It could also be had on the higher trim W body Grand Prix GXP
You can check the code for the suspension you have, and replace the worn out parts with originals, or possibly upgrade some of it to the next level.
I went all the way from "mush" to "ouch my back hurts" in my 04 LeSabre. Looks stock, but has the whole Bonneville GXP suspension under it, which took a bit of time and money to find. But, there aren't a lot of upgrades for our cars in the aftermarket.
That said, no its not that bad on the back. It corners like you wouldn't believe, and I scare the crap outta people who don't realize a Buick can be made to handle. I'll assume you start with FE1, as I did. Replace the struts in the front, shocks in the rear. They are probably worn out, hence the floaty feeling. Then get an SSEi front and rear sway bar and some good Moog end links and new mount bushings.
The biggest difference came from the sway bars when I did my swap. The shocks and strut combos were good. But the difference really wasn't felt until the bars went in.
2004 Buick LeSabre Custom FE5 GXP suspension conversion. 170Kmi
2001 Silverado 4WD 5.3L, 33" BFG ATs, Z71/Z82 pkg, 147kmi.