I notice that a lot of teenagers that play guitar or bass don't know much about recording at home. Specifically about interfaces, microphones, hardware, amps and software that can help them achieve this. When I was growing up I bought a Zoom H4 when they first came out. It is a hand-held 4 track recorder with 2 inputs and 2 condenser mics in XY for recording stereo. I put this in front of my guitar amp and connected a pair of headphones to it for monitoring. These days you can do multitrack recordings on an iPhone using garage band (see my other recording interface blog). There are other apps like MTSR that turns your phone into essentially what was my Zoom H4 for free. Firstly: To get a decent sound that is able to be edited you are going to want to invest in an interface. Most likely a USB interface that comes packaged with some guitar modelling (amps and effects). The first thing that springs to mind is the Line 6 POD range. There are a few different models in this line ranging from a 1 input Studio GX guitar interface or a POD 2.0 to a 2 input UX1 or UX2 (mic and guitar) interface. Buy them brand new for $150-$300 or hunt around on Ebay for a deal.
Past the POD's are Native Instruments line of Guitar Rig which retails for $299. But then you will need an interface. (See my interface blog for more info).
There are lost of entry level setups for guitarists that are on a budget. Big companies don't realise the potential market for upcoming teenage guitarists that have a few hundred dollars to expand their guitar possibilities.
You can't go wrong with a line 6 pod. The only other thing I would suggest is invest in a decent USB mic and something like a Fender Mustang. This amp has a decent array of effects in it but you can come into trouble if you don't know what you are doing. These types of fender amps tend to be quite trebly and need to be EQ'd properly. Fender Mustang amps also have USB compatibility which is handy to plug it into your computer.
You can achieve quite a lot with 1 decent mic and an amp that has some digital effects and I think that the earlier you get into playing around with FX on a guitar. The earlier you will start painting your own tones and figuring out what you like as an artist.
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