Noisy TH3

Does your guitar have unshielded single coil pickups?
If so the pickups are picking up noise from your computer.

I have problems with my strat clone due to that issue.
I have to angle my guitar just right or the noise is overwhelming.

I haven't used TH3 yet but this problem exists for all amp sims. When you pump up the gain you are boosting the input signal along with all of the noise that is present in that signal. Things like USB cables, guitar cables, hot pickups, interference from computer monitors, WiFi antennas, bluetooth antennas, noisy interface preamps, etc. all add to this noise floor and are amplified right along with the sound of the guitar. You can try things like moving your interface as far from the computer as possible, turn off bluetooth and WiFi if it's a laptop, experiment with different pickup configurations if you have a switch but you will still may need to add a gate to the beginning of the plugin chain. The thing that made the biggest difference for me was a new interface.

The problem occurs with amps and pedals as well as sims.

If you use a lot of gain/compression that boosts the noise coming from the guitar itself and any pedals before the gain is added.

Gates are a last resort fix that’s rarely satisfactory, and they always affect both the attack and sustain of the guitar.

Humbucker-equipped quitars shouldn’t be as noisy as single coils, but even a well shielded guitar with good humbuckers will still pick up some electrical buzz from sourounding stuff. Guitar leads also pick up noise and can act as ariels, especially with some pedals such as simple fuzz circuits. Computers put out a lot of electrical noise as radio which guitars pick up and send to the amp. Changing the angle between guitar and computer/monitor can sometimes make for a big decrease (or increase) in the noise picked up by the pickups.

Paying attention to gain staging can go a long way towards minimising noise. E.g. running a distortion pedal that boosts the signal a lot and creates noise itself into another similar pedal, compressor or a high-gain amp is a recipe for a lot of noise. For minimal noise, pedals that generate noise are best used into cleaner amps that boost the noise floor less than a high gain amp channel. The ideal is to get the noise floor as low as possible by better gain staging and then consider gating as a last resort. A gate that only affects certain frequency bands, such as a couple of Bozdigital’s, can be useful on guitar and be much less obtrusive than a full-frequency gate.

It does have to be said that some amp sims are very noisy themselves, maybe even noisier than the amp they are trying to emulate. Same with some effects emulations, which start with over the top settings and noise levels. The Amplitube Big Muff being an example of one.

Put the Expander/Gate module in the Pro Channel Rack.
Do it RIGHT NOW!
I had the exact same problem with Amplitube.
The Expander/Gate module was INCREDIBLE!!!!!!!
Problem GONE!!!!!!!

TH3 has a very nice gate that will cut out hum quite well.  A real amp is much more difficult to control than TH3.  Set the gate so that it's quiet between notes but will stay open during sustained notes.  Thedoccal's advice is good, too, and you may prefer to use both gates.  Hope this helps.

A low pass filter with a cutoff between 4 to 5k (you can experiment) often can tame unwanted frequencies, too.

I swear amp sims make this buzz worse though. My Telecaster buzzes far more loudly when plugged into an amp sim than it does plugged into a real amp with similar settings, even with my guitar in exactly the same position. I just presumed it was one of these stupid attempts by developers to make plugins sound more "real" by adding noise, and that they add too much. I cannot use higher gain amp sim presets unless I rotate my guitar into just the right position, which annoyingly enough happens to be facing away from my DAW with the body tilted down to the floor about 30 degrees. I literally have to play like that lol. 

Its not always guitars in particular, though I know what 60 cycle hum sounds like coming from a strat.
Most of my good starts I modded with grounding shield (copper paint/copper tape).
More often than not its the Amp sim itself and its only using high gain amps and/or associated with gain pedals in general.
When im using high gain Amp sim models I always use a gate. most have them built in to the amp sim for this reason alone.

Double post courtesy of the laggy forum software, ignore.

tlw
I've come across people on forums who have only used sims then finally got a real JCM or Mesa who complain their amp is broken because it doesn't have the "killer distortion" of the emulator's version of that amp.

Most of those people have what is called a bad ear, tainted by the use of Amp Sims.
But seriously though, I don't know anyone who owns a JCM, Plexi or Mesa Boogie that prefers Amp Sims over the real McCoy (unless its necessary for late night recording, scratch track ideas).
 
Amp Sims have come miles in just the past 3 years alone. But they can not and never will be better than the real thing. I own many amps, microphones and speakers (for different head/cab combinations) and I have yet to find an amp sim that replicated the sound of tube break up like a real JCM800. Positive Grid Bias comes pretty darn close but just like sampled drums, I will always take the real thing over a modeled amp.