What you need is a decent mid range editor from Corel or Sony. You would record the main part and afterwards the solo.
These editors have a main timeline track and (what are called) overlay tracks. Your main guitar part would sit on the main timeline and the solo part on an overlay. You can move the part on the overlay to align with any frame on the main so that it looks like one piece. That covers the video and you can do exactly the same with the audio.
The camera is more difficult given your budget. Yes the internal mics will give a very reasonable result as long as your recording location is free of noise but, ideally, a camera with an external mic socket would be better so that you can locate a stereo mic (camera mic sockets are normally 3.5mm stereo) close to your guitar. If your guitar has an electric pick up then a direct connection to the camera is possible BUT you would need a bit of electronic kit to make the guitar signal compatible with the camera mic input. If the pick up is of a microphone type than you would probably be OK.
Hello. I would like to sync two separate video recordings of me playing the guitar. The first would be of the main guitar part. Then I would like to go back and record a guitar solo and add it to the main recording such that it is in time with the first guitar recording. Please tell me how to get started. I was hoping to stay under $200 for a camcorder. I also want something small that I can take on hikes. Thanks.

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