#1
I've been looking for a way to get my guitar through my headphones without sounding like ass, I have neighbors and a whiny brother. I recently bought a Marshall Code 25, which sounds decent, but when I go to the neck pickup on my guitar and play on the low strings, it just sounds like a hand put over someone's mouth. It even affects the higher register if you play the higher and lower at the same time. This is very annoying because I'm interested in 7/8 string guitars.

Budget is €300-400. It doesn't have to have a good speaker, I can pretty much only play on my headphones due to complaints. It can also be a multi effects processor, like an ME-70.

Stuff I had in the past I didn't like:

Marshall Code 25
Line 6 Pocket Pod
Line 6 spider IV
Guitar Rig 5 (Always got digital noise, maybe because my interface: M-Audio M-track)

What I would like the most is a multi effects unit with an amp simultaor that is capable of recording to pc through USB. It MUST be able to record in some way.
#2
You have a lot of options here.  

1. Another MultiFX but a higher quality one like a Line6 Pod HD500X, Helix (out of budget), or Atomic Amplifier (out of budget).

2. A quality interface or at least something that doesn't have latency (i've gotten good results with a RockSmith USB Cable into a MacBook Pro).  The Scarlet series are normally well regarded but I've never used one.  

3. Quality amp sims, effects, and speaker impulses. I use Peavey ReValver and it does great for what I need.  

4. A "studio" amp that has a USB interface and headphone output with speaker emulation built-in.  I use a Laney IRT-Studio and it works really well for this.  The built-in speaker emulaion could be better though IMO.  Peavey has several options in their MH line - 6505, ValveKing, Classic.  

5.  A combination of things - for instance I'm really liking the Laney IRT-Studio hooked into the computer via USB into Reaper but using the speaker/cabinet impulses from ReValver.  I pull the headphones out of the computer.   This way I have a 3 channel tube amp with all of my physical pedals and loop but with better speaker emulation. It's obviously more to hook up than just the instrument to USB cable but the experience is different with tactile knobs and buttons.  Plus I can hook the Laney up to real speaker cabinet and it's just like any other amp. . . 
Guitars:
Jackson Kelly KE3 - MIJ (Distortion/Jazz)
Jackson DKMGT Dinky (EMG 81/85)
ESP E-II Eclipse Custom (JB/'59)
ESP LTD EC-1001FR (EMG 81/60)
Fender MIM Strat

Amps:
Mesa/Boogie Dual Rectifier Roadster 212
Laney IronHeart IRT-Studio
Peavey Vypyr 30
Peavey ReValver Amp Sims
TOOOO many T.C. Electronic Pedals. . .
#3
Pod Bean, Pod HD, Vox Tonelab, Helix, iphone/Garageband, and many others.  Lots of good choices to get great guitar tone over headphones as long as you use them within their design parameters.  Use a digital device outside it's design envelope will quickly disappoint.  Most bad experiences when using quality DMFX devices is simply user error.
"Your sound is in your hands as much as anything. It's the way you pick, and the way you hold the guitar, more than it is the amp or the guitar you use." -- Stevie Ray Vaughan

"Anybody can play. The note is only 20 percent. The attitude of the motherfucker who plays it is 80 percent." -- Miles Davis

Guthrie on tone: https://www.youtube.com/watch?v=zmohdG9lLqY
#4
Quote by Cajundaddy
Pod Bean, Pod HD, Vox Tonelab, Helix, iphone/Garageband, and many others.  Lots of good choices to get great guitar tone over headphones as long as you use them within their design parameters.  Use a digital device outside it's design envelope will quickly disappoint.  Most bad experiences when using quality DMFX devices is simply user error.


I started out with a Korg Pandora PX5D (battery powered, cigarette box size, tons of features, USB recording, etc.) and picked up a Pod bean XT. The current Pod HD bean also ticks all your boxes and you can graduate to using it live with an FBV Shortboard II. Well within your budget, I've seen used ones popping up at $200-250. 

If you're using any of these with a set of four buck earbuds, however, you're not going to get anything worth while going forward. My suggestion is always that you should be looking for a set of studio-standard on-ear or over-the-ear headphones that do NOT emphasize bass. You should budget $100 - $200. My go-to candidates have been things like the Sony 7506 (studio standards forever), AKG 240, Sennheiser 280, BeyerDynamic 770.  Most "Beats" or DJ-style headphones won't cut it. 
#5
Like dspellman, I started with a Korg Pandora (Px4, then Px5), and continue to use them to this day. I also have a MFX unit with a headphone jack- Digitech's discontinued iPB-10.

However, I don't spend big bucks on headphones because I found out that many manufacturers will sell refurbished units for ridiculously low prices. A decade ago, i bought a half dozen refurbished over-ear style Sonys for $5 each (original price @$80+). Kept one for myself, gave the others away. I'm getting ready to retire them, but I already have their replacements in hand. IOW, do get good headphones, but don't necessarily spend big bucks on them. Deals can be had.

I've also found that the march of technology has helped the headphone-using guitarist even more, I'm seeing more amps- tube and SS- with headphone jacks. You might like a Quilter 45 or 101. Solid state, non-modeling amp that takes pedals well, and has just such a jack.

http://www.quilterlabs.com/index.php/productpage/microblock-45
http://www.quilterlabs.com/index.php/productpage/101-mini-head
Sturgeon's 2nd Law, a.k.a. Sturgeon's Revelation: “Ninety percent of everything is crap.”

Why, yes, I am a lawyer- thanks for asking!

Log off and play yer guitar!

Strap on, tune up, rock out!
#6
Quote by Cajundaddy
Use a digital device outside it's design envelope will quickly disappoint.  Most bad experiences when using quality DMFX devices is simply user error.

How do you mean using it outside it's design? 
#7
Zoom G3/G5.
Gibson LP Traditional, LP GT, LP Studio, SG Standard x2
Barber Tone Press > EHX Worm >TC Polytune > MXR Custom Badass 78 > EXH Glove > EHX East River Drive > Zoom G3 > TC Spark Mini Booster
Laney VC30
Marshall TSL602
Jet City JCA22H
.
My SoundCloud