Is RIT dye any good?

I want to dye a vest that I bought at a thrift store and altered (it started out a boring men's vest, and now it's very cute, if i do say so myself!) black. Right now it is grey wool (or something similar) on the front and brown silk (or similar) on the back. I have seen RIT dye before, but never used it, so i was just wondering if it'd be any good for this or if you know of another inexpensive (since the whole point of going to a thrift store in the first place is that I'm cheap and crafty) textile dye. Also, i hear you use it in our washing machine. Is there any danger of this dye staying in the machine and ruining future clothes? Should I do a rinse cycle after I dye?