Absolutely. Not all fans are created equal, but most fans will become effectively silent if you turn down their speed, even the junk usually included with cases. Fans generally have one of two connectors, either a 3 pin with +, - and RPM monitoring, or 4 pin, called PWM. All modern boards should be able to control either type via the fan headers.
All fans have different noise characteristics and one that sounds pleasant to my ears may not to yours, but we're probably going to mostly agree on what fans sound good and what don't. Not all fans will slow down equally though. Some will go as low as maybe 3.5v, while others may stop spinning at close to 7v. I've found that most stock case fans tend to either have audible humming from the hub, or will "click" when slowed down. If your fans do this, come back and ask about replacements, but I'd try just controlling the speed via bios first. Your noise threshold may be higher than mine.
The Intel stock cooler tends to run a bit on the warm side, but the noise characteristics are actually pretty great. I wouldn't bother replacing it for an i3.
To get a bit more in depth, there are two main bearing types in fans, sleeve, and ball. Sleeve bearing fans tend to be quieter (that is, less clicking and hum, you still hear the air moving equally), but don't last nearly as long, especially if not mounted vertically because of how lubricant is distributed. Yate Loons are a very popular case fan that are often regarded as having excellent noise characteristics, and are typically $3-6 each. I have a box full of them (maybe 20-30), but unfortunately after a few years most begin to degrade and get noisier. I recently replaced all of the fans in my case with Noctua fans, which run $15-20 each. There's debate on whether or not they're a good value, and you'll find little love for them in places like SPCR (mostly due to price), but my experience with them has been overwhelmingly positive, price aside. They have a 6 year warranty and come with a ton of connectors and rubber mounts for noise isolation. You could buy 3-6 Yate Loons for the same price as a single Noctua, of course.
If silence is worth a lot to you, you may want to read reviews on power supplies first and pick one that's quiet out of the box, as their fans are a bit more complicated to replace.
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