Re: what recording program to use?
I would recommend trying Reaper. It is easy to use, a very small file, runs incredibly efficient, stable, updated often, has a lot of excellent effects and has an amazing user forum. Oh, and it is free for the first 30-days! After that, it has a pop-up screen, but everything still works. A non-commercial license only costs $40 (USD). I have been using Reaper for a while now, and it is worth well above what they are charging.
I would not recommend plugging your amp into your computer's mic socket unless the amp is designed for that type of setup. You may want to try plugging your guitar into your computer's line-in socket and using some of the Reaper effects (also known as "plugins").