Turrntable With or Without Suspension?

I agree with the prevailing sentiment here. A suspended table is probably not going to solve your problems as you describe them. I have what I consider to be one of the best suspended tables available but I know that if the whole foundation that it is sitting on is moving all the suspension in the world will not fix that. That is not what a suspended table is designed for.

I'll pose a different solution. Mass. No, not the state. A very heavy, sturdy, massive stand with a non-suspended table. You may have to DIY a stand like this, unless you can afford one, and then couple the table to it with good spikes.

Or, you have to move to another room that is off-limits to the rough housers.

I used to have an HK/Rabco ST-8 on top of a shaky wood cabinet, all on a suspended wood floor. The TT had a rudimentary suspension (putting it kindly) and would skip any time someone moved a teacup, never mind kids bouncing around.

Big fat Sorbogel footers helped some but it was still pretty bad. If you wanted to walk while a record was playing you truly had to baby your way around. One normal step and it would skip.

As the others have said, the scenario you describe seems basically untenable. Something has to give.

I second the B&O suggestion. Many years ago I had the same problem but, instead of foot falls, it was trucks on the road outside that were causing the problems. The Technics couldn't handle it so I went to a B&O radial tracker. (I think it was a Beogram 5000?) I don't know how they did it but you could slap that thing around all day long and it wouldn't skip or send footsteps through the speakers. Mid-Fi but, a used one should be well within your price range. First you might want to check on availability of cartridges as the low mass tone arm could only accept special B&O units.

We had a suspended thorens 166. Tried a DIY high-mass stand. And just like some of the other responses any time someone tip-toed around the living room or even shut the front door the stylus would skip. It was pretty bad until we got the wall shelf. But even with the wall mount you could stll hear outside rumble (traffic, passing trains, airplanes) through the table. You have to be careful where you put the table.

If you have a crawl space under the house, you might be able to prop-up or otherwise support the floor just below the turntable stand to help damp the footfalls somewhat. Rather than let that area be super springy.

Ngeorge:

My table's a Russco Cuemaster broadcast turntable. Popular in 70s and 80s especially on west coast, which is where it was built (Fresno/Clovis, California, just a drive down I-5 from where I was born and raised). The design matches other broadcast tables like Gray Research, etc. Built like a tank.

Being a large idler wheel table with a powerful motor, it wants to be mounted in a massive stand, hence the monolithic plinth I built. More info on my table project here:
http://www.stat.ucla.edu/~erickson/projects/cuemaster/

It does not cast "ink black" backgrounds, but its virtues more than make up for that, in my book at least.