I'm working pretty much how you want to -- live guitar, bass, vocals, and percussion, with drums and other instruments programmed.
For that sort of music, you don't need to go overboard recording hundreds of tracks (I rarely use more than 20-30), so any relatively new computer should be able to handle it. I had my local computer place build me a machine, so I've got a PC with an Intel Core i7, a 250 gigabyte solid state drive, a 1 terabyte regular hard drive, 16 gigabytes of RAM, and running Windows 7. I find this is more than good enough for recording, if you don't go overboard with the number of tracks and effects plugins.
At this point in time, I'd still be going for a decent USB 2 interface. That's the safe option. There are dozens of these available. And I think a newer one will probably give you better sound-quality than the old Tascam. But personally, I wouldn't bother upgrading the Tascam for a cheap entry-level interface. If money's an issue, I'd put off upgrading until I could afford something with a bit of quality, like an RME or MOTU interface.
For microphones, I'm not sure I'd go with the NT1-A, which is notorious for being overly bright and harsh. I'd go for the new NT1, and with the money I saved on that, get an SM57 as well. The SM57 is going to sound better than any condenser if you want to mic a guitar amp.
For software, I'm using the full paid-up version of Zynewave Podium. It's cheap and it's simple, but it's designed for exactly the kind of recording you and I are doing (i.e. mostly live tracks mixed with a few programmed VST instruments). There's a free version you can try, if you want to check it out. It might not be the all-singing all-dancing kool-kidz DAW of the minute, but it beats the heck out of trying to do multi-tracked recordings with Audacity.
For the PC, there's a free version of a DAW called "Podium" which looks good. But I'll agree that Audacity and Reaper are great. Both will work on Mac and PC.
Audacity is really simple to use but doesn't quite act like a typical DAW and is kinda limited in what it can do. If you've used Garage Band and Reason OK, you may be ready for something more sophisticated.
Podium: http://zynewave.com/podium-free Audacity: http://audacity.sourceforge.net/ Reaper: http://www.reaper.fm/
It's the one that's actually free, instead of nudge-nudge wink-wink say-no-more "free". And it still has the best user interface of any DAW I've ever used.
All of us who do music seriously make a bit of extra money on the side doing related things. I work in a rehearsal studio. The guitar player in my band busks. I know other guys who teach guitar and drums. It's not an industry to get into if you want to be rich.
There's a few DAWs that have usable free versions with a limited number of tracks and features:
Here's Podium (PC only) http://zynewave.com/podium-free/
MuLab has a nice simple layout (Mac & PC): http://www.mutools.com/info/docs/mulab/mulab-versions.html
There's a free version of ProTools called "ProTools First". However, they limit you to 3 projects before you have to pay. http://apps.avid.com/ProToolsFirst/
You can start with Zynewave Podium free, which is a sleek, cut-down DAW with all the features you need and no limitations that matter (i.e. no DRM, and no limits on the number of tracks and buses).
If you're really new and don't want to spend any money yet, I can't recommend Zynewave Podium Free enough (as long as you are running a windows system that is). It is a superb DAW with a really intuitive workflow and it supports audio and MIDI. It can host VST and VSTi effects and instruments and IT'S FREE!
I use it and love it but you do have to do a bit of legwork to track down midi instruments (VSTs) as it doesn't come bundled with any.