You would be doing yourself a huge favor by starting with a so-called modelling amp, like the Fender Mustang, Peavey Vypyr and Roland Cube (they all have one thing in common: They can emulate other amps, though they may not make it obvious which ones they're emulating). I personally play through a Fender Mustang II, which I love, but both the Roland Cube and Peavey Vypyr are quite good too.

The Roland Cube is one of the most popular solid-state amps around where I live. I personally didn't really like its interface that much, but it's a pretty good amp anyway. I don't know if it has a USB-connection, though it would surprise me if it doesn't. I've only played it once or twice, though.

The Peavey Vypyr is another pretty good (quite low-budget) amplifier. I don't know a lot about it other than that, though. I've seen them at a pretty low price where I buy gear, but they sound really nice. I considered buying it instead of the Fender, but its presets were a bit confusing to my. It probably has a USB-connection as well.

Finally, there's the Fender Mustang Amplifiers. As mentioned earlier I play through a Fender Mustang II, but the only real difference between I and II is that I has a smaller speaker and half the Watts compared to II. All Fender Mustang amps have a USB-connection, which you can use to turn it into a recording interface, or use a program called Fender Fuse to change the settings in the amp (on II, there's no physical Middle-knob, so to adjust that as well as effects, Fuse is necessary, which I consider it's only problem). It also has a few built-in effects that can actually sound surprisingly good, considering the price. They don't beat physical Pedals, though, in my opinion.

I could easily talk for minutes about the Fender Mustang, since I'm by now fairly familiar with it. I don't know enough about the Roland Cube or Peavey Vypyr to judge which one is best out of the three. You'll have to try them all for yourself in a store (or get an employee to help you), before you buy. It's no good to just pick the one that looks coolest if you don't like its sound or if you can't figure out how to operate it properly.