Nick mentions the iRig. The more expensive of the two, c/w belt clip controller is a wonderful thing. Especially the feedback buster. It costs around £60 online and to be honest, I use it with a guitar that has a perfectly good Fishman Sonitone pickup installed but the iRig has a more natural sound.

Mic for guitar can sound wonderful and I do for studio use. I run the sound desk for a concert venue and as we have a “proper” stage, mic can work. However, beware using one in a smaller setting as background noise and indeed feedback can be an issue. Many professionals on the circuit are using a single ribbon mic for guitar and voice nowadays, to wonderful effect. But these guys still know where such things should be used or not...

If you insist on mic use and you can’t guarantee the 48v phantom that condenser mics need, I suggest a Shure SM57 or equivalent. But such a purchase makes the iRig a no brainer both costwise and performance. It is, after all, a form of microphone.