Hi matconstanzo,
There are many options for recording guitar:
1. Digital amps like the BOSS Katana have USB audio connections built in. This is probably the easiest option nowadays and you might find it's cheaper than buying good equipment for recording an analog amp.
2. Place a microphone in front of the speaker. This is the traditional approach to guitar recording. A popular microphone is the Shure SM-57. It can be connected to a USB audio interface.
3. There are reactive load boxes with cabinet IR simulators like the Universal Audio OX (
https://www.uaudio.com/hardware/ox.html) or cheaper options. They basically allow you to record a guitar amplifier without playing at loud volumes. Some require a separate USB audio interface.
4. Plugging the guitar cable directly into a USB audio interface will let you record the dry signal and then use software amp simulators like Scuffham Amps S-Gear for the amp and effects - jammr can load VST plugins and AudioUnits. Or if you don't want to be tied to a computer you can get a little pedal/box the does the amp simulation like the Atomic Amps Ampli-FIREBOX or the Line6 PocketPOD.
There are many options depending on all the ways you'd like to use your gear and your budget. Try watching product reviews on YouTube so you can hear how these options sound and see how the work.