Would changing to H&R lowering springs stiffen the ride of my Toyota Innova? It's a single-person car during weekdays, and a family car of five adults and two kids on weekends. Should I also change the stock shock absorbers upon installation of these springs or can I still use the stocks until worn out?
In general, when you shorten the suspension travel of any vehicle--like if you install a set of lowering or sport springs--this will result in a firmer ride. There are instances, however, particularly on models that have been equipped with what most car manufacturers call a "rough or off-road suspension package," when the ride will actually be perceived to be better than when it was stock.
I don't know if the local Innovas come equipped with that kind of suspension. And I haven't had the opportunity to ride one with H&R springs either. I suspect that when you're driving by yourself in the car, you will most likely not complain about the ride in general. On rougher roads, you might want to slow down a bit more than usual for the potholes and bumps as reduced suspension travel will increase the probability of bottoming out the suspension (fully compressing the suspension rapidly and hitting the bump stops hard).
Fully packed, there's a good chance that you'll want to upgrade your shocks to something that's more suited to the springs you plan to install, more so if your Innova is a few years old and the suspension has seen some wear and tear.
Personally, one of the first few things I upgrade on the vehicles I own--apart from better tires and brakes--is the suspension, either with a shock/spring combo or with a set of adjustable damping coilovers. I don't do it for the cosmetics though; I do it to tune the suspension more to my liking, which is to say for better roadholding and handling than what the stock suspension has to offer.
If you like driving, nothing beats a vehicle that handles well. I hope I haven't left you more confused than you already were.