#1
I'll be moving into a apt. in the next day or so and my amp has no headphone jack. is a headphone amp the answer, if so how do I sit it up? can I still use my petals?
#2
The Vox amphone are nice, I was gonna buy one myself but it was out of my price range, I got the AC30 amplug they make instead, the tone is a bit weak at times, feels flat, but is perfect for rare days when I don't want to piss off my neighbors.

As for the pedals I think it's possible, the headphones come with an 1/8" jack but I believe they come with a 1/4" adapter to plug in to your guitar, so you should be able to plug it through multiple pedals. If it muddies up the sound quality I couldn't tell you, but I would think it'd work out fine.
#3
I'd recommend a Zoom G3/5, and use that for all your effects & your amp sim. It also includes a looper that synchronises with the built in drum sequencer, which is a great feature for practicing with.

It's also more than good enough to gig with should the need arise (my G3 has a permanent place on my pedalboard), and can be plugged direct into a PA so you can use it as a backup to your main amp.
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
#5
DannyAlcatraz should be by in a bit with a whole selection of choices.

I use a Korg Pandora (I have both PX5D and PX3D models) -- there's a "MINI" version that runs about $99 retail that's got most or all of what the PX5D has in it. All of these have amp/cab/FX simulators in droves, plus a whole lot of practice bits and pieces, such as a Slower Downer (slows down the song without changing its pitch so that you can play along at a slower pace while you're learning), a pitch changer (some songs are released in Eb, for example, but you may want to learn it in E), a phrase trainer (plays the same section of a song over and over so that you can practice specific passages), a tuner, a set of drum tracks, another set of bass tracks and so on. They even have a place for you to plug in your iPod so that you can play along with anything on your phone, pad, pod, etc.

And the little one runs on a single AA battery.

And then, of course, there are adapters that allow you to use specially designed apps on your hone.
#6
I play and record through a Boss Micro BR 80. It has so many features and the recording s are great with it. Recording is a lot of fun with it. The Micro BR has just about all the effects you need I have been making a lot of my own patches even have a fake organ patch using rotary speaker.
You will be surprised by how powerful headphones amps are these days.
#7
Just to chime in... I use a Pod X3 from Line 6. I love it, it's got tons of amp + cabs models, effects, and a dual tone path so you can for example have one amp panned to your left ear and another one panned to your right ear. Done right it can sound pretty awesome... excellent recording quality as well...
#8
Just did a quick test. My Sansamp Character works fine with headphones, so it can do double duty as a versatile OD/distortion stomp box and headphone amp. The only problem is that, being mono, it only delivers to one ear from a standard 1/4" stereo headphone jack. It would need a stereo to mono adapter for both ears.
#9
You can't really beat digital for silent and quiet practice. Line 6 offers modeling units from $129 (pocket pod) up to $500 for a HD500X... and of course there always lots of there old stuff on the used market.

Other companies that make this kind of stuff are digitech (RP and XP series), Zoom, Roland/Boss.

You can put pedals in front of any of these although results may vary. Running a boost pedal to overdrive a tube amp sounds good; overdriving a digital unit and getting input clipping sounds very bad. You'd need one of the more expensive varieties to get an FX loop if you run pedals that way.
2002 Gibson Les Paul Studio
2014 Fender Strat (American Nitro Honeyburst)
2003 Ibanez Acoustic
Digitech RP500
Blackstar HT5R