Cubase (paid) is another very popular digital audio workstation like Pro Tools or Reaper.
I have worked with Cubase and Reaper before, but not in a video game music context, and both of them get their job done. They are easy to use with virtual instruments (VSTi plugins) and MIDI files, too - overall I think MIDI/VSTi stuff is a bit quicker on Reaper than on Cubase, but I haven't delved too far into it yet.
Guitar Pro (paid) or its free clone Tuxguitar are great tools for composing MIDI from a guitarist's point of view.
As far as actual vocal recording and mixing go, I LOVE Cubase. Its extremely easy to use and the built in tools and plugins are some of the best out of the box in the industry IMO. I also shelled out the $900 for Pro Tools 9 and almost never use it.
You are fine with a laptop. You need a multi-input interface to allow you to mic drums separately or record more than one musician at a time. HERE is a cheap one. You need some sort of multitrack recording software. You can look at Reaper which is very nice and very cheap. You could look at Cubase which is more money and may or may not be better. And then there are 58 million other ones. Since you already have mics and other supportive items, that's about all you really need.