The Babyface's Hi-Z instrument input is 470KOhms according to the specs in the manual. Which is perhaps a little on the low side, 1MOhm or higher being generally considered a better match for the input impedance of a valve amp.

Having said that, 470KOhm is also the input buffer's impedance of a Tube Screamer and people generally don't complain about Tube Screamers affecting their tone for the worse when switched off. If you've any pedals that have buffers between guitar and interface the guitar will see that buffer in any case, not the Babyface's impedance. A good DI box with a 1MOhm+ input impedance might get you a bit more volume and treble, but so would any Boss pedal put between guitar and interface (Boss pedals all have 1MOhm buffers which are pretty good as it happens).

The additional buzzing compared to what you might get in stage is almost certainly down to being near a computer. Computers can emit all kinds of radio interference which single coil pickups are very susceptible to receiving. Add flourescent/low energy lighting, domestic lighting dimmers, switching power supplies, electrically noisy transformers in monitor amplifiers etc. into the equation and noise can quickly get out of hand.

A DI box won't reduce noise unless there's a ground-loop between two mains-powered pieces of kit when the earth-lift switch on the DI might make a difference.

The best answer to single coil noise is to first try having the guitar at different angles to the computer, monitor screen etc. and see if that helps, or to get the guitar further away from the sources of electrical noise. It might also be worth shielding the pickup and control cavities with copper foil or conductive paint connected to earth, though Fender have been applying conductive paint to the cavities in many of their instruments, even the less expensive Mexican ones, for some time. The usual give-away that this has been done at the factory is a wire screwed into the pickup or control cavity, or trem spring cavity on a Strat.

As for Teles and high gain, a Tele+fuzz->Marshall setup is as old as fuzzes and Marshalls. Or overdriven tweed Fender amps. You'll probably always get some noise, because a Tele bridge pickup in particular is quite a bit more powerful than the anaemic Strat vintage single coils, and a Tele Texas Special is about as powerful as a PAF humbucker and can really buzz away.

It's even quite possible the guitar is just as noisy on stage - it's just that playing live we and the audience tend to filter out the noise, it's only when recording or listening to a recording we spot it.

Yeah I have experimented with guitar positions in the past and funnily enough there are a couple of positions in my room which are substantially quieter - unfortunately they both involve me facing away from my DAW, quite a distance from it.

I might look into a preamp to improve my tone however. Any recommendations?

sharke
Have no experience with them. Would a good pro-quality DI box reduce buzzing and improve the general tone of my Telecaster into my Babyface?

A "vanilla" DI box won't really affect the tone.
A-Designs Reddi Box and Avalon U5 are examples of DI boxes that are designed to enhance the sound.
 
When recording near the computer, true single-coil pickups are going to pickup EM noise.
You can minimize it (shielding the pickup cavity, turn away from the computer when recording, etc)... but you can't completely eliminate it.
 
Rather than a higher-end DI, I'd checkout some "noise-less" pickup options.
This won't completely eliminate noise... but it'll stop most of it at the source.
 
MusicMan is using an active noise-reduction circuit in their single-coil guitars.  
Works surprisingly well...

Jim Roseberry

sharke
Have no experience with them. Would a good pro-quality DI box reduce buzzing and improve the general tone of my Telecaster into my Babyface?

A "vanilla" DI box won't really affect the tone.
A-Designs Reddi Box and Avalon U5 are examples of DI boxes that are designed to enhance the sound.
 
When recording near the computer, true single-coil pickups are going to pickup EM noise.
You can minimize it (shielding the pickup cavity, turn away from the computer when recording, etc)... but you can't completely eliminate it.
 
Rather than a higher-end DI, I'd checkout some "noise-less" pickup options.
This won't completely eliminate noise... but it'll stop most of it at the source.
 
MusicMan is using an active noise-reduction circuit in their single-coil guitars.  
Works surprisingly well...

I did think about looking into shielding, yeah. Any little improvement will help. I'm taking my Telecaster in for a setup soon so I will ask the guy what he can do. 

For my Strat, changing to some Fender Custom Shop noiseless signal coils totaly worked with sitting close to my workstation. It did not ruin the Strat tone and now it's almost dead quiet.  Many companies make noiseless signal coils. 
My G& L Astat ( Tele)  which had SC soap bars was also very noisy. I put some GFI humbuckers but it changed the tone to much so I'm looking into something better. Harder to find Soap Bar's. But there are many regular Tele upgrade Pups on the market. If I change the pickguard I can just use regular Tele Pup's. 

Fender's various generations of noiseless pickups are very much a love/hate thing.

I tried a set of vintage noiseless on a Mexican Strat which came with ceramic bar magnet pickups that were a bit like a poor copy of a P90 and buzzed like mad. I hated the vintage noiseless. Sounded a bit Strat-like but bland and even with the 1 Meg volume pot provided by Fender still sounded to me like the low output humbuckers they are and acked top end ring and bite. Then tried the Fender hot noiseless set and hated them. In the end I settled on Lace Sensor Hot Gold which cut the buzz down hugely while still having the vintage Strat openess, chime and quack, and drive pedals better than Fender's Strat single coils.

Just my personal preference...

I have EMGs in an AM BC Rich ST in a SSH configuration. They are OK, very quite. I have Bill Lawrence PUs to replace those, but haven't installed them yet. I put Joe Barden PUs in my strat and like those. A friend has Lace Sensors, but they have too much bite for my taste. As tlw says "personal preference".

You don't need a DI box if you use the BF's high impedance input.
 
If you were trying to e.g. plug a guitar straight into a mixer input, then you'd need a DI box to perform the required impedance matching; without this you'll lose the high frequency response and volume of the guitar signal.
 
As a general rule, the impedance of an input should be the same as or higher than the impedance of the output.
 
Guitars with active pups generally provide a low(-er) impedance output, but it's still desirable to plug them into a high impedance input.
 

a DI has questionable benefit in your case..
you can..
a) copper foil shield your cavities
b) change to noiseless pups
c) get a pod, modeling setup, preamp or other means to quietly record..
 
but, at the end of the day, it is far easier and cheaper to use your phone as a remote for Sonar and play in a position and orientation in your studio that mitigates noise..
 

For players of acoustic guitars, DIs can help with very high impedance.