Hey Will:
You already have a good start; I've always used my hi/fi system's integrated amp as the heart of my mix-down after I've cut a tune.
Depending on your budget and ears, all you need is an 8 track box; there are several on the market. You need to research to find which one suits your needs and learning curve.
Also, if you have a penchant, say, for the Roland line, you can rent one to see if it works for you. Then, you can shop the 800 numbers to get the best price and dealers do vary more than 100 dollars on certain items.
Also, you can go via PC and a packaged system to record; so, look around and shop around and have fun recording because it is fun to "finally" produce a cool cut.
The Green Hornet