BIAS is coming to iPhone sometime this week.
JamUp and BIAS are apps on iPhone or iPad. Made by the same company, JamUp is all inclusive; amps, ODs, delays, etc...BIAS is an app that lets you design your won 'amps' based on existing designs; there's Diezels and 6505s and Matchless and 5153s and a bunch of Marshalls and pretty much everything else. You can swap OTs and tubes and power tubes and whatnot, and then drop those amps you make into JamUp and use them in that app.
Apogee Jam is the interface that a lot of us use; guitar>Apogee>iPad/iPhone>JamUp. It works well and does exactly what it's supposed to do, and it's around $100 new and $60 or so used. There are other interfaces, but they lack. The Line6 SonicPort is another good one, and there are a bunch more if you wanna go higher end, up to an Apogee desktop version that runs around $1200. You aren't going to be able to use your TC.
There is an app called Audiobus that acts like virtual cables in your iPad and lets you chain other music apps to JamUp and use them as well, and then you can run JamUp/effects apps/GarageBand to record.
GarageBand for iPad lets you upload finished stuff or demos to Soundcloud from your iPad, or save them and transfer to a bigger DAW to do other things.
For live use, you'd need a guitar, interface, the apps, and some kind of power amp and cab; you can disable the cab in BIAS and run it thru a regular head and cab as well.
Any other questions feel free to PM. I've been using it for awhile and dig it a lot as a low cost all in one recording solution.