For home use, what you list is probably just fine. Like Lonman said, through, for the money, you could do much better. As a general rule, anything marketed as a "karaoke" product is about twice the price and half the quality of good, name-brand live music equipment. Find comparable items from Yamaha, Wharfdale, JBL, DB Technologies (one of my favourite British distributors), Mackie, D&B, RCF, EV, Peavey, even Samson and Behringer for home use.
After all, despite LOTS of opinion to the contrary, karaoke IS LIVE MUSIC!!
Check out this link:
http://www.stagebeat.co.uk/index.php?page_id=554
Most of those packages would be great for home use. Just add a karaoke CDG player, and you're good to go!
Anyway, if I were you, I'd stick with lower-end equipment while you are just starting out, and focus on learning how to use it and what EVERYTHING does, and how to troubleshoot problems. When you are comfortable that you have the hang of it, and you have that system sounding AS GOOD as it possibly can, given its limitations, you will also know what those limitations are, and you can start upgrading components one by one.
Warning, though, once you pop, you just can't stop! Most of the people on this board will be upgrading PA system components until the day they die!!