Definitely recommend you spend your money on PA speakers.
You are going to need some sort of mixer. The Denon thing you have is probably a DJ mixer, and not really the kind you want for karaoke.
You don't really need the Lexicon Alpha. While it is a very fine sound card, the sound card on your PC will be fine for this purpose. If you later become a connoisseur, then add the Lexicon at that time.
One possibility is buying a pair of cheap "DJ" speakers like:
http://tinyurl.com/3enw85wYour receiver should drive them, though 70w is on the low end of what you need. Combine them with a Yamaha MG82CX and a mic ranging from $80-100, and you have a usable setup that can sound decent for about $450. And you'll avoid blowing your home theater speakers, which is the usual outcome when you try to use them.
I would go with the laptop. Downloadable karaoke is very available, for reasonable cost, and you can pick the songs you want one by one instead of buying a large number of filler songs you won't use. If you are having parties, you could consider buying a set like Supercore to give your guests something to sing. We had our first party with just Supercore, and it worked fine.