There is poor and good quality suspension, and big travel and small travel suspension. First, let's eliminate poor quality - that is a gimmick. That leaves small vs large travel. For road riding, large travel has to be argued as being not necessary.
Chucky is absolutely correct that the very first line of defense against road bumps lies in tyres. Modern hype makes many riders over-inflate tyres leading to unnecessary harsh riding. Every tire has its optimum pressure setting, that should be used. Fat tyres due to generally weaker casings, employ lower pressure, giving a plusher ride. Narrow tyres have stronger casings because they need higher pressure to prevent pinch flats. This usually also leads to lower rolling resistance as there is less flexing in the casing. A tyre that is pumped even harder actually feels faster but careful testing has shown that to be not a real effect when the tyre is already pumped to a suitable pressure.
So the tyres are small travel suspension, with no weight penalty.
It is possible to use narrow high pressure tyres and combine that with small travel suspension to remove the harshness. That can actually lead to lower rolling resistance over uneven ground, as only the wheels have to be lifted over bumps instead of rider+bike. That sort of suspension is no gimmick. It also gives greater comfort than tyres alone.
So, avoid buying a bike with poor quality suspension - it will give you info as to the rest of the bike's quality.
The best approach is to start looking at bikes with no suspension - best bang for buck as good suspension costs lots.
If the bike as-is is too harsh, the next step is to get some plush tyres, and here Big Apples is the final name. Others also work very well, such as the Scorcher already mentioned. That should fix you up.