For recording i use OBS. It's free and a lot of people use it. Alternatively you can use software which your videocard provides like shadowplay.

For editing software i've used Hitfilm. It works great and you can do just about everything you want with it. It does lag a little bit when editing so for that reason i'm now trying out Adobe Premiere. I feel you can do a bit more in hitfilm than in purely adobe premiere, but the full adobe suite (particularly after effects and photoshop) does provide a lot of functionality i use.

For a mic i use a blue snowball ice mic. So far i've gotten plenty of compliments on my mic and audio quality, and judging by most reviews it's a great mic for the price (got it for about 50 bucks).

I've never had any audio foam, and have tested with some blankets and stuff, but i find being in a smallish room and making sure you're very close to the mic is enough. Some work in audacity can do the rest.