I just did a similar upgrade to Michelin Primacy MXM V4 (V-rated version) in the same size as you 195-60/15. My 2011 Base had just over 17K miles on the original Dublops and, while they looked fine and likely to last another 10K at least, I felt they were sub-par on wet and in cornering and emergency maneuvers.
The Michelins were $124 each delivered from Discount Tire Direct (similar price from TireRack on sale). And no, we do not need valve stems - the tire pressure sensors already have them, so don't order! There is a $70 rebate from Michelin, so the cost will be just over $100 per tire (before installation). I got the V-rated version, which was just a few bucks more than the H version (about $5 difference per tire). Plus $100 to install locally, so all said and done about $520.
There are cheaper alternatives, but I like to get tires with the highest available traction and temperature ratings on the sidewall and that do well in tests and user reviews

I debated to also upgrade the rims to 17" and go for 205 sized tires (which would have further improved handling) but decided against that expense, since the rest of the car does not really do "justice" to such a package without additional mods (such as lowering and sway bars), and which I have not enough enthusiasm to do
Oh, and they balanced perfectly and ride smooth with no vibrations, which was a big concern for me. I've had problems with Continental and Sumitomo tires that would balance perfectly but would still vibrate at speed (on the same wheels/cars where a set of Michelin Pilot Exalto would run smooth). So, one of the reasons I went for the Michelins here too - I hate vibrations at speed and one aspect of the Dunlops was that they were extremely smooth on my Insight at speed and I did not want to lose that...
I put them on the stock steel rims a couple of days ago, and indeed I can confirm that they do not look too odd (I was afraid that due to the 5.5" narrow rim and the added 20mm width on the tire they would bulge, but they don't). The front tires now fill the wheel wells more towards the outside, which I don't particularly like, but not obnoxiously so. The point is that if one considers even wider tires on new wheels, they need to make sure they get the right offset wheels so that the wheel do not stick out too much. I measured roughly the space around the stock wheels/tires (was considering to upgrade the rims to 7" wide 17" diameter too) and there did not seem to be much extra space in several areas - one reason I did not go with wider tires/rims as rubbing would be very likely.
Handling is different - less wobble in turns, more secure. Straight line is not necessarily better though. I never had issues with tracking on the straights with the original tires, and if anything, with these wider tires I feel the Insight requires more corrections to keep a straight line when there are slight valleys from heavy traffic on the pavement. This is just a function of the width of the thread - a narrow tire just tracks better in a straight line when the road surface under the wheels is a little tilted. I've noticed that with my other cars as well. When the pavement is flat, the car tracks fine with no corrections needed (as it did just fine with the old tires too). The difference is when maneuvering at speed, where the car is a bit more planted with less wobble side to side.
Steering is still light (I was afraid it might become heavy and strained, especially for parking and slow speed maneuvers).
These tires are also more quiet on all surfaces. Fuel economy is hard to judge, but in a week or two I will report when I refuel again. Seems perhaps a minor drop of about 2mpg but the pressure on the new tires is 38psi (lower than before), where the old were 44 or so - have not gotten a chance to go top the new tires up to about 40 or 42... Probably there will not really be too much penalty.
Because these tires are Grand Touring (and I'm used to having ultra or high performance versions on my other cars, which are generally sportier) I did not see such a marked improvement as I would expect to get from a sportier set. And also because they are similar sidewall height as the stock tires, I would not really describe the improvement as "monumental". Yes, the car is more quiet, yes road imperfections do not transfer nearly as bad, yes it corners and stops better. All good things and clearly better than before. But the car is still riding on narrow 15" wheels on a tall and soft suspension, so one can't expect miracles by just changing the tires. An incremental improvement, yes...
The Insight still does not handle nearly as well as it could with say 16" or 17" and wider wheels, and perhaps an inch of suspension drop, but still by jsut changing the tires, the ride has improved noticeably in pretty much all respects.