You playing thru an amp, or strictly headphones?
I've gotten decent results playing with headphones thru a smartphone. When it comes to amp modeling, you can get a multi-effects rig from various sellers like Line6, Digitech, etc. I really like an app for my PC called S-Gear by Mike Scuffham (google it). His amp models are quite excellent! If you want to jump off the deep end, there's the boutique stuff like Fractal Audio Axe FX or Kemper. WAY more than I would recommend for a beginner (or most amateurs, really).
There's really nothing like that 'amp in the room' sound and response however. Then you've got to decide if you like the pristine cleans of a Fender, the chime of a Vox, the fantastic dirt of a Marshall, etc. You can change the character of your tone with pedals into your amp as well. Overdrive for a little grind, or Distortion for over the top gain, Fuzz for that unique vibe- etc. The you can delay (echo) your tone, reverb it, or modulate it.
What a fantastic hobby! I've been in love with the guitar forever. What a great vehicle to express yourself!
Thanks mate, I'm just playing it without it plugged in to anything at the moment though I do have a big old bass amp that my mate is storing at my house indefinately if I want to muck about. One of the reasons I bought electric was it can be quite quiet so I can practise any time I feel like it without disturbing the wean or the missus too much, that and most of the music I really like us electic guitars. My birthday is in a few months and the family are always looking for a few gifts so a small amp will be going on that which will do me for mucking about. I've already got plans for a few mods, though I'll play it plugged in for a bit but I'm quite technical by nature and a precision engineer by trade so I'm not afraid to get stuck in to mods.
I'm a metal fan primarily so the marshalls sound great to me. Though I do like the blues as well and my favorite guitarist is Hendrix (hence why it was important to me to buy a fender as my first guitar, plus I have a mate that is an excellent guitarist and I remember back in the day when he got a fender USA strat and I really liked the way the body felt, it was just kinda "right" if you know what I mean. Very ergonomic). I do remember the old vox amps sounding good, though a bit indie for my taste.
I'd be interested to hear how you would put one through a phone to headphones? That could be very interesting indeed!