If you are going with an inverter, find what's called a "true sine wave" inverter.
But be forwarned, they are not cheap.
The cheap ones are modified sine wave and while they will work, it's very "messy" power and some of the more delicate electronics don't like the format.
The main issue with inverters is the power draw results in less battery endurance time when using the comp when the car is off. Yes, they also generate more heat than a dc-dc supply. Most people don't like the process of converting DC power to ac power to only convert it back to dc power for the comp. I'll admit, it is ineffecient. Also, the more......errrrr......... "particular"....... people here will call it "ghetto".
As to noise, it's kind of a crap shoot. Depends on the quality of the inverter and your install.
I'm using an inverter right now and I have no issues at all. But I was very careful with my install and wire routing.
A dc-dc solution is more effecient and elegant, but sometimes it is not for everyone (my board is not atx standard, I'm still cyphering it out and will probably go dc-dc when I can).
If your board is an atx standard, I'd say spend a few bucks and get a properly rated dc-dc supply. A true sine wave inverter is going to cost you as much as a dc-dc solution (and you still need a start/shutdown controller). Most of the dc-dc solutions offer built in startup and shutdown controllers by design.
So if you look at it from a "total dollar expenditure" stand point, the dc-dc solutions are actually cheaper than running an proper inverter setup. And more effecient.